DAY 200

Your job is to deliver 100 crystal glasses to a fancy party. You will be paid $3 for each glass delivered intact, but you will forfeit $9 for every broken glass. You earned $240. How many glasses did you break?

Answer:

5...........Let G = the glasses delivered intact and B = the glasses broken.
3G - 9B = 240
G+B = 100
3(100-B) - 9B = 240

DAY 198
A girl was 8 years old on her first birthday. How?

Answer:

She was born on February 29, 1996. (2000 was not a leap year.)

DAY 199
Truth or Lie: The day before yesterday I was 17. Next year I will be 20.

Answer:

Truth.......My birthday is December 31. I am telling you this on January 1. The day before yesterday (Dec. 30) I was 17. Yesterday (Dec. 31---my birthday) I was 18. I am telling you this on January 1, so this year (on Dec. 31) I will be 19, and next year I will be 20.

DAY 196

THE CLEVER KING
20 artisans worked for a king making various pieces of gold jewelry. Each piece was supposed to weigh exactly 1 ounce. The king learned that one of the artisans was making his pieces consistently 1/8 oz. less and stealing the difference. The king was able to identify the culprit in only one weighing. How did he do it?

Answer:

The king took one piece of jewelry from the first workman, two from the second, three from the third, and so on. In total, the king had 1+2+3+4+5.......+20 or 210 pieces. If all were full weight, they would weigh 210 ounces. If the first artisan were cheating, the total weight would be short by 1/8 oz. If the second artisan were cheating, the total weight would be off by 1/4 oz. (2 x 1/8). If the sixth artisan were cheating, it would be off by 3/4 oz. (6 x 1/8), etc. Whatever number multiplied by 1/8 was equal to the shortage in the total weight would be the number of the cheating artisan.

DAY 197
The following addition problem uses each of the digits 1 - 10 once. What else is unusual about this problem?

35/70 + 148/296

Answer:

The sum is 1...........each term equals 1/2.

DAY 193
What number is as much greater than 36 as it is less that 94?

Answer:

65..........X-36 = 94-X

DAY 194
A farmer said that 1/5, 1/6, and 1/7 of his flock when added together would equal 107 sheep. How many sheep did he have?

Answer:

210 sheep............1/5 + 1/6 + 1/7 = 107/210. If N = the number of sheep, 107/210 N = 107.

DAY 195
If you double 1/5 of a fraction and multiply it by that fraction, you get 1/10. What is the original fraction?

Answer:

1/2.........2(1/5)N x N = 1/10

DAY 191
Fred's father agreed to pay him 10 cents for every correct math answer, but would fine him 5 cents for every incorrect answer. After working 24 problems, Fred was paid 15 cents by his father. How many of his answers were correct?

Answer:

9...........10X - 5(24-X) = 15

DAY 192
Tom S. Windler had $5.00, but he needed $6 to buy a baseball glove. He went to a pawnshop and pawned his $5 bill for $4. Next he sold his pawn ticket to Jerry for $2. Tom then had enough to buy the glove. Who lost on this deal and how much?

Answer:

Jerry lost $1. He had to pay $4 to redeem the $5 bill, and he had already given Tom $2 (not including any service fee which might be charged by the pawnbroker).

DAY 189
Want to gain instant celebrity in the world of mathematics? Prove "Goldbach's Conjecture," advanced in 1742, which states that every even number larger than 2 can be written as the sum of two prime numbers. Try it with 16, 38, 82, and 174

Answer:

16 = 5 + 11
38 = 19 + 19
82 = 29 + 53
174 = 47 + 127

DAY 190
What number must be added to 1/4 to get 2/7?

Answer:

1/28............2/7 = 8/28......... 1/4 = 7/28

DAY 187
I am a 3-digit number. My tens' digit is 5 more than my ones' digit. My hundreds' digit is 8 less than my tens' digit. Who am I?

Answer:

194

DAY 188
You go shopping. At the first store you spend 1/2 of your money plus $5. At the second store your spend 1/2 of what is left plus $4. At the third and final store you spend half of what remains plus $3, after which you have $5 left. How much money did you start with?

Answer:

$90........Let X = the amount of money you have as you enter each store. Working backward, at the third store, X - X/2 - 3 = 5. Solving this, you had $16 as you entered the third store. This means you left the second store with $16. X - X/2 - 4 = 16, you had $40 as you entered the second store. This means you left the first store with $40. X - X/2 - 5 = 40, you had $90 as you entered the first store.

DAY 185
Four oranges and six apples cost $1.30. Six oranges and four apples cost $1.20. How many oranges can you buy for $1.00?

Answer:

10.........10 oranges and 10 apples cost $2.50. So an orange and an apple cost $.25.
The conditions of the problem could only be satisfied by an apple costing $.15 and an orange costing $.10

DAY 186
Which is greater: the number of seconds in 100 hours, or the number of inches in 100 yards?

Answer:

Seconds in 100 hours----by a factor of 100----3600 inches in 100 yards---coincidentally the same as the number of seconds in an hour.....360,000 seconds in 100 hours.

DAY 183
What number when divided by 5 gives the same result a when 5 is subtracted from it?

Answer:

6.25...........X/5 = X - 5

DAY 184
What comes next in this sequence: A 31.....S 30.....O 31.....N 30..... _____?

Answer:

D 31.........December---31 days

DAY 181
Three bags of jellybeans and two bags of chocolate chips cost $24. Two bags of jellybeans and four bags of chocolate chips also cost $24. How much is it for one bag of chocolate chips?

Answer:

$3.........Let J = jellybeans and C = chocolate chips.

3J + 2C = 2J + 4C

J = 2C

3(2C) + 2C = $24

8C = $24

C = $3

DAY 182
1/3 of a number plus 3/4 of the number less 1 equals the number? What is the number?

Answer:

12

DAY 179
A dozen, a gross, and a score,
Plus three times the square root of four.
Divide by seven,
Plus five times eleven,
Equals ____ squared, and not a bit more.

Answer:

9.........

12 + 144 + 20
+3(2) = 182
182/7
+ 5(11)
=26+55
=9 squared (81)

Credit: Leigh Mercer
from Word Ways - Feb. 1980

DAY 180
A certain month will begin on Friday and end on Friday also. What month is it?

Answer:

February in a leap year...........Friday to Friday is 7 days. The last day of the month must be 28 days from the first day. 28+1=29---February 29.

Day 176
Jack and Jill collect shells. At the start of their vacation, Jack had 380 shells and Jill had 29. Each day of their vacation, Jack found 21 shells, and Jill found 48. At the end of their vacation, Jack and Jill each had the same number of shells. How long was their vacation?

Answer:

13 days.........Let X = the number of days of their vacation. At the end of their vacation, Jack had 380 + 21X shells, and Jill had 29 + 48X shells. Since they ended up with the same number of shells, these two expressions equal each other. To solve the problem without algebra: 380 - 29 = 351......the difference in the number of shells between Jack and Jill. 48 - 21 = 27........the difference in the number of shells collected each day. 351 divided by 27 = 13.

DAY 177

14 x 82 equals 41 x 28---1,148. Likewise, 39 x 62 = 93 x 26---2,418. Why does this work?

Answer:

In each case, you get the same number of ones, tens, and hundreds. (1x8=4x2 and 3x6=9x2)

DAY 178
What patterns do you notice in the difference of the squares of two consecutive numbers?
4 squared - 3 squared = 16 - 9 = 7
5 squared - 4 squared = 25 - 16 = 9
6 squared - 5 squared = 39 - 25 = 11
7 squared - 6 squared = 49 - 36 = 13

Answer:

If you go in order, the differences are the consecutive odd numbers, and, regardless of order, the difference of the squares of two consecutive numbers is equal to the sum of those two numbers.

DAY 174
Rewrite the equation 1/27 + 1/27 + 1/27 = 1/9, so that only one of the denominators is 27.

Answer:

One soulution: 1/18 + 1/27 + 1/54 = 1/9

Day 175
What whole number divided by a whole number equals 1.818181..............?

Answer:

20/11................Let X = 1.818181 and 100X = 181.818181. Subtracting gives 99X = 180.0000. X = 180/99 = 20/11

DAY 172
If you repeated the sequence ILOVEMATHEMATICS, what would be the 948th letter?

Answer:

V...........948/16 = 59 remainder 4............ V is the fourth letter in the sequence.

DAY 173
In the equation 1/X + 1/X + 1/X = 1/9, what is the value of X?

Answer:

X = 27.........3/X = 1/9

DAY 170
From a plate of cookies, Person A took 1/3 of them, Person B took 1/3 of what was left, and Person C took 1/3 of what was left after Person B. After Person C took his third, 8 cookies remained on the plate. How many cookies were on the plate to start with?

Answer:

27............If X is the number of cookies on the plate when Person C takes his third, then X - 1/3 X = 8. This means there were 12 cookies on the plate before Person C took 4 of them. The equation for Person B would be X - 1/3 X = 12, or 18 cookies on the plate before he took 6 of them. For Person A.........X - 1/3 X = 18, or 27 cookies on the plate before he took 9 of them.

DAY 171
What is the sum of the products in the 9's times table.........(9+18+27+36+45+54+63+72+81+90)?

Answer:

495............By pairing the numbers 0-9/1-8/2-7/3-6/4-5, you get five groups of 9 each = 5 x 9 = 45 in the ones' column, which becomes 49 in the tens' column. Another approach is to realize the products represent 1 nine, two nines, three nines.......up to ten nines. Since the first 10 numbers add up to 55 (ten groups of 11 each), 55 x 9 = 495

DAY 168
A two-volume set of books stands on a shelf in the usual manner---Volume 1 to the left of Volume 2, the bindings facing out. The pages of each book are 3 inches thick, and the covers are 1/4 of an inch thick. A bookworm starts on the title page of Vol. 1 and eats through to the last page of Vol 2. How far did the bookworm travel?

Answer:

1/2 inch.........With the books in the standard position, the first page of Vol. 1 is next to the last page of Vol. 2. The bookworm only ate through the two covers.

DAY 169

A train signal light turns red every 6 minutes, another every 8 minutes, and a third every 10 minutes. At 2:00 p.m. all three signals are red. At what time will this next happen again?

Answer:

4:oo p.m.---------The LCM of 6, 8, and 10 is 120. 120 minutes = 2 hours.

DAY 166
A man buys a book for $6 and pays with a $10 bill. The clerk doesn't have change, so he goes to the neighboring shop and gets change for the $10. The customer leaves with the book and $4 change. Later the clerk discovers the $10 bill was counterfeit. Naturally, he must repay the $10 to the neighboring storekeeper. How much was lost in the transaction?

Answer:

$4 and the book

DAY 167
One train leaves New York for Baltimore and travels at 25 mph. At the same time, another train leaves Baltimore for New York and travels along a parallel track at 50 mph. When the two trains meet, which is nearer to New York?

Answer:

This is a classic trick problem. When the two trains meet, they are the same distance from New York (or anywhere else).

DAY 164
What number when added to itself, subtracted from itself, multiplied by itself, and divided by itself will add up to 64?

Answer:

7 or -9..........A number subtracted from itself is zero, and a number divided by itself is one........... X squared + 2X +1 = 64...........This can be solved either by factoring or by taking the square root of each side.

DAY 165
A school cafeteria buys hot dogs in packages of 36 and buns in packs of 20. What is the least number of each that can be ordered so that you have the same number of hot dogs as buns?

Answer:

5 packages of hot dogs and 9 packs of buns...........The LCM of 20 and 36 is 180.

DAY 162
64 meters of fencing was needed to enclose a square garden. What is the area of the garden?

Answer:

256 square meters............the square must have a side = 16 meters

DAY 163
You have three boards. One is 39 inches long, the next is 52 inches long, and the third is 65 inches long. What is the greatest length into which these three boards may be cut so that they are all the same length?

Answer:

13 inches............the greatest common factor of the three numbers

DAY 160
From Ask Marilyn by Marilyn Vos Savant:

A nanny with four small children passes a bubble-gum machine, and all four children beg for a gumball. However, the nanny knows they will cry unless they all receive the same color. The machine is almost empty, and she can count eight pink gumballs, six blue ones, and one green one. At a penny apiece, how much money is the most she might have to spend to get four matching gumballs?

Answer:

eight cents..........With the worst possible luck, the nanny could spend seven cents and end up with three pink gumballs, three blue ones, and the one green one. With a penny more, the next gumball would be pink or blue, making the fourth match.

DAY 161
A freight train one mile long is about to enter a tunnel that is one mile long. If the train is traveling at a speed of 15 miles per hour, how long does it take for the train to pass completely through the mile-long tunnel?

Answer:

8 minutes............15 mph equals 1 mile every 4 minutes. After 4 minutes, the train will be completely inside the tunnel. It will take another 4 minutes for the train to completely exit the tunnel.

DAY 158
What is the sum of the first 100 counting numbers?

Answer:

5,050...........This is a classic math problem. The trick is to put the numbers into pairs from 1 to 100 such that each pair adds to 101. (1+100.....2+99.....3+97............
continuing to 50+51) Thus 50 pairs of 101 each = 50 X 101 = 5,050. A simpler example of this is to add the first 10 counting numbers (1+10.....2+9..... continuing to 5+6) Five pairs of 11 each = 5 x 11 = 55.

DAY 159
A bus with no passengers on board makes its first stop and 5 people get on. At the next stop 8 people get on. At the next stop 6 people get off. How many people are now on the bus?

Answer:

8........7 plus the driver.

DAY 156
Ann, Betty, and Claudia live in adjoining apartments. They work as a chemist, a doctor, and a lawyer, though not necessarily in that order. Find each woman's occupation from the following clues:

Betty lives in the middle apartment.
When Claudia goes on vacation, the lawyer feeds her cat.
The chemist taps on Ann's wall when her stereo is too loud.

Answer:

Betty is the chemist, Ann is the lawyer, and Claudia is the doctor. Only Betty, in the middle apartment, could tap on Ann's wall. (It is impossible to determine who lives to the right or left of Betty.)

DAY 157
In a dish of red, yellow, and green M&M's, all but four are red, all but four are yellow, and all but four ae green. How many M&M's are in the dish?

Answer:

6...........(X-4) + (X-4) + (X-4) = X

(2 of each color)

DAY 154
Think of this as a column addition problem.

OH + OH + OH + OH = NO

What is the value of O, H, and N?

Answer:

O = 2
H = 3
N = 9...........23 + 23 + 23 + 23 = 92

DAY 155

AB + BA = 66
A = B + 2
What is the value of A and B?

Answer:

A = 4
B = 2.........42 + 24 = 66

DAY 152
The Pupils of Pythagoras:
Q. Tell us, illustrious Pythagoras, how many pupils frequent they school?
A. 1/2 study math, 1/4 natural philosophy, 1/7 observe silence, and there are 3 girls besides.

Answer:

28..........1/2 X + 1/4 X + 1/7 X + 3 = X

DAY 153
If you add the digits 1 through 9, the answer is 45. By changing just one of the plus signs to a multiplication sign and adding a single pair of parentheses, the sum is now 100. What is the change?

Answer:

Put parentheses around the 8 and 9 and multiply them.

(28 + 72 = 100)

DAY 150
If 1 1/2 men can eat 1 1/2 pies in 1 1/2 minutes, how many pies can 3 men eat in 30 minutes?

Answer:

60.........1 man eats 1 pie in 1 1/2 minutes, so he can eat 20 pies in 30 minutes. Three men can eat 20 x 3 = 60 pies in 30 minutes. Or 1 man can eat 2 pies in 3 minutes......or 20 pies in 30 minutes.

DAY 151
Using only addition, make eight 4's equal 500.

Answer:

444+44+4+4+4 = 500

DAY 147
If A + B = 18 and A X B = 72, what is A squared + B squared?

Answer:

180..........A and B must be 6 and 12. (8 + 9 does not equal 18)

DAY 148
Why should you never use the number 288 in public?

Answer:

It's too gross...........(2 x 144 = 288)

DAY 149

What is the next number in this series?
1.....8.....27.....64..... ___

Answer:

125..........the perfect cubes

DAY 145
In the problem A + A + A = BA, what is A and what is B? (This is a column addition problem. BA is a two-digit number---not B x A.)

Answer:

A = 5 and B = 1.........5 +5 + 5 = 15

Day 146
In the problem AB x A = 111, what is A and what is B? (AB is a two-digit number.)

Answer:

A = 3 and B = 7...........37 x 3 = 111

DAY 142
If to my age there added be,
One half my age, one third my age,
And three times three,
Six score and ten the sum will be,
What is my age? Pray show it to me.

Answer:

66.......X + X/2 + X/3 + 9 = 130

DAY 143
If 3 salesmen can sell 3 stoves in 7 minutes, how many stoves can 6 salesmen sell in 70 minutes?

Answer:

60........One salesman can sell one stove in 7 minutes. In 70 minutes, one salesman can sell 10 stoves......six salesmen can sell 60 stoves

DAY 144
A man, his wife, and their two sons must cross a river. The man and woman each weigh 100 pounds, and the two boys weigh 50 pounds each. The rowboat can only hold 100 pounds at a time. All four are capable of rowing the boat. How do they all get across the river?

Answer:

The two boys cross first. One boy brings the boat back, and either the mother or father crosses. The other boy brings the boat back. Both boys cross again. One boy brings the boat back and the second adult crosses. The other boy brings the boat back and the two boys cross for the third and last time.

DAY 139
A pile of boards each 3/4 inch think is 8 feet high. How many boards ae in the pile?

Answer:

128 boards

DAY 140
A box of books weighs 50 pounds. Each book weighs 1 3/4 pounds and the box itself weighs 8 pounds. How many books are in the box?

Answer:

24 books

DAY 141
Which is greater? The number of seconds in a day or minutes in a 30-day month?

Answers:

Seconds in a day---by a factor of exactly 2..... 43,200 minutes in a 30-day month; 86,400 seconds in a day.

DAY 136
Using only addition, make five 1's equal 14.

Answer:

1 +1 + 1 +11 = 14

DAY 137
How many trees would have to be planted on a street 40 yards long if there was a tree every ten yards on both sides of street?

Answer:

10 trees.........5 on each side

DAY 138
The Miller's Toll by Henry E. Dudeney: A miller was accustomed to take as toll 1/10 of the flour that he ground for his customers. How much did he grind for a man who had just one bushel left after the toll had been taken?

Answer:

1 1/9 bushels..........X - 1/10X = 1

DAY 133

What is the next number in this series?
1...1...2...3...5...8...13...21... ___

Answer:

34........Add the previous two terms to get the next term (Fibonacci Series).

DAY 134
What number is missing in this series? Can you see two different patterns?
1...4...9...16... ___ ...36...49...64

Answer:

25........the perfect squares or adding the consecutive odd numbers

DAY 135
On a tray of muffins, if you divide the number of muffins by 3, there is one left over. If you divide by 4, there is also one left over. But if you divide by five, there are none left over. What is the smallest number of muffins that could be on the tray?

Answer:

25............The answer must be a multiple of five.

DAY 130
Two shepherds owning a flock of sheep agree to divide its value equally. If one takes 20 sheep and the other 30, and the latter pays the former $150, what is the value per sheep?

Answer:

$30..........The first 40 sheep can be disregarded because they are divided equally 20/20 between the two shepherds. It appears the second shepherd is paying $150 for the remaining 10 sheep, which of course would mean the value of each sheep is $15. But in fact the second shepherd is entitled to 5 of those sheep by the terms of the equal division of the flock. So he is paying $150 for 5 sheep. Another way to think of it is to divide the flock equally 25/25 between the two. The second shepherd is buying 5 sheep from the first for $150.

DAY 131
A printing press can print 6 pages every 1 1/2 minutes. How many 30-page reports can it produce in 2 hours?

Answer:

16

DAY 132
My birthday is in March. If the date were a fraction.........month/day............it would be equivalent to 159/477. When is my birthday?

Answer:

March 9.......since March is the third month, 3/X = 159/477

DAY 128
You have scored an average of 16 points in 5 games. The first four games you scored 22, 21, 15, and 10 points. How many points did you score in the fifth game?

Answer:

22...........To average 16 points in five games, you must have scored 90 points. You scored 68 points in the first four games, meaning you must have scored 22 points in the fifth game.

DAY 129
Two dogs eat a 1 1/2 lb. of dogfood every 2 days. At $2/lb. how much does the dogfood cost in a 30-day month?

Answer:

$45

DAY 126
The denominator of a fraction is greater than its numerator by 6. If 8 were added to the denominator, the value of the fraction would then become 1/3. What is the fraction?

Answer:

7/13............X/X+6 +8.........X/X + 14 = 1/3

DAY 127
A farmer was asked how many animals he owned. He replied, "All but 20 are cows, all but 18 are horses, and all but 14 are sheep." How many animals did he own?

Answer:

26............(X-20) + (X-18) + (X-14) = X

DAY 124

Two bicycle riders are 60 miles apart. They begin riding directly toward each other. At the same instant, a fly leaves the front tire of one of the bicycles, flies directly to the other bicycle's front wheel, instantly turns around and flies back to the first bicycle, and continues this until the bikes meet and the fly is unceremoniously squished. If the bicycles travel at 30 mph and the fly flies at 15 mph, how far will the fly have flown when it is squished?

Answer:

15 miles.........The two bicycles are approaching each other at a combined speed of 60 mph. This means it will take them one hour to meet. The fly will fly 15 miles in that hour.

DAY 125
How can you cook an egg for exactly 15 minutes if all you have are two uncalibrated timers, one that runs for 7 minutes and one that runs for 11 minutes? (Think of the timers as sand hourglasses.)

Answer:

Start both timers at the same time. When the 7-minute timer runs out, start cooking the egg. When the 11-minute timer runs out, the egg will have been cooking for 4 minutes. Immediately turn over the 11-minute timer to give you 4 + 11 = 15 minutes.

Alternate solution:
Credit GAMES Magazine
November, 1983
Steve Odell

Start cooking the egg and turn over both timers at the same time. When the 7-minute timer runs out, turn it over to start timing again. When the 11-minute timer runs out, the 7-minute timer will have been running for four minutes. Turn the 7-minute timer over again. After another four minutes, the 7-minute timer will run out. 11 minutes + 4 minutes = 15 minutes.
(posted 2/17/16)

DAY 122
You have nine identical coins. One of them is just slightly lighter than the other eight. How many weighings on a balance scale would it take to determine the lighter coin?

Answer:

2..........Weigh 3 against 3. If they do not balance, take 2 from the lighter side and weigh them against each other. If they balance, the third coin is the lighter. If they don't balance, the lighter coin is obvious. If the 3 against 3 weighing balances, follow the same procedure with the remaining 3 coins.

DAY 123
Divide 59 into two portions such that the sum of 1/7 of the greater portion and 1/3 of the lesser equal 13.

Answer:

35 and 24............1/7X + 1/3(59 - X) = 13

DAY 120
Find the number whose double is greater than its half by 45.

Answer:

30...........2X = X/2 + 45

DAY 121
A well is 10 feet deep. A frog at the bottom climbs up 5 feet during the day, but falls back 4 feet during the night. On which day does Froggie get to the top?

Answer:

On Day 6..........On the fifth day the frog has climbed 5 feet. On the sixth day he climbs five feet to the top (ten feet) and climbs out.

DAY 118
There are nine judges on the Supreme Court. If they each shake hands with each other, how many handshakes are there?

Answer:

36........8+7+6+5+4+3+2+1...........or 9 X 8 divided by 2

DAY 119
A farmer has two uncalibrated containers. One holds five quarts and the other holds three quarts. The farmer has an unlimited supply of water in his well. How can he measure out exactly seven quarts of water?

Answer:

Fill the 5 qt. and pour it into the 3 qt. until it is full. This leaves 2 qts. in the 5 qt. container. Dump out the 3 qt. container and pour the 2 qts. into it. Fill the 5 qt. giving you 2 + 5 = 7.

DAY 116
The difference between two numbers is 3, and the difference of their squares is 51. Find the numbers.

Answer:

7 and 10..........(X + 3) squared - X squared = 51

DAY 117
FInd four consecutive numbers totaling 94.

Answer:

22, 23, 24, and 25

DAY 113
Split up 34 into 2 parts so that 4/7 of one of the parts equals 2/5 of the other.

Answer:

14 and 20.........4/7X = 2/5(34-X)

DAY 114
What number is equal to the sum of 1/3 + 1/10 + 1/12 of itself plus 58?

Answer:

120..........X = 31/60X + 58

DAY 115
11 x 11 = 121..........111 X 111 = 12321...........What is 111,111,111 X 111,111,111 ?

Answer:

12,345,678,987,654,321.......12 quadrillion, 345 trillion, 678 billion................

DAY 111
A number plus 4/7 of that number equals 27 less than twice the number. What is the number?

Answer:

63........X +4/7X = 2X - 27

DAY 112
What day was the day before yesterday if the day after tomorrow is Sunday?

Answer:

Wednesday

DAY 109
The average age of 10 people is 20. When Mr. Dee Krepit is added to the group, the average age is 25. How old is Dee?

Answer:

Dee is 75 years old..........for the average age of ten people to be 20, their ages must add up to 200. For eleven people to average 25, the total ages must be 11 x 25 = 275.

DAY 110
You have 45 candy bars. You are going to have a party, but you want to give the same number of candy bars to each guest. What are your choices as to how many people to invite to the party?

Answer:

You could invite one really good friend and give him all 45 candy bars, 3 friends and give them 15 each, five for 9 each, nine for 5 each, fifteen for 3 each, or 45 guests and give each person 1 candy bar.

DAY 106
A customer handed a bank teller a check for $210 and asked for equal numbers of $10 and $20 bills. How many of each did he get?

Answer:

7 of each..........10X + 20X = 210

DAY 107
The sum of two decimals is 9.3 and their difference is 4.3. Their product is 17.00. What are the numbers?

Answer:

2.5 and 6.8..........the problem can be solved with just the sum and difference.

DAY 108
Find two factors of 10,000---neither one ending in zero. Same thing for 1,000,000.

Answers:

16 and 625

64 and 15,625

DAY 103
Counting at the rate of one number per second, and never stopping, how long would it take you to count to 1,000? 1,000,000? 1,000,000,000?

Answer:

1,000 seconds = 17 minutes
1,000,000 seconds = 12 days
1,000,000,000 seconds = 33 years

DAY 104
Two friends, Sharon Sharealike and Ima Hogg, have the same number of marbles. Sharon has 2 bags and 2 marbles. Ima has 1 bag and 7 marbles. Each bag contains the same number of marbles. How many marbles are in each bag?

Answer:

5..........Bag + Bag +2 = Bag + 7

DAY 105
A recycling plant gives 1 free bottle of soda pop for every 5 recycled bottles. How many free sodas would you get if you recycled 77 bottles?

Answer:

19.......77/5 = 15 free bottles + 2 left over......15/5 = 3 free bottles + the 2 left over..... these 3 + the 2 left over make 5.......these 5 yield 1 free bottle: 15 + 3 + 1 = 19

DAY 101
Two friends, Ira Member and Joe King, were running as fast as they could. They averaged 6 miles per hour, and then had to rest. On the way back, they averaged ony 4 miles per hour for the same distance. Not counting resting time, what was their average speed?

Answer:

4.8 miles per hour........If they ran 12 miles each way, it would have taken 2 hours up and 3 hours back............5 hours to run 24 miles.

DAY 102
The NASA Space Shuttle uses 1,000,000 gallons of fuel in the first 81/2 minutes of flight and reaches a speed of 25,ooo miles per hour. What is its fuel efficeincy? (Assume a constant speed of 25,000 mph.)

Answer:

Approximately .002 of a mile per gallon, or 500 gallons per mile.

DAY 96
Two numbers are reciprocals of each other. One number is 9 times as large as the other. What are the two numbers?

Answer:

3 and 1/3..............X = 9/X

DAY 97
Each page of a book has 100 rows with 50 dots in each row. The book contains 1,000,000 dots. How many pages are there in the book?

Answer:

200 pages

DAY 98
A pen costs a dollar more than an eraser. Together they cost $1.10. What is the price of each?

Answer:

$1.05 for the pen and $.05 for the eraser.

DAY 99
By what number would you multiply 692 to get 692,692?

Answer:

1,001

DAY 100
How long will it take to cut a 10-foot piece of wood into 10 equal pieces if it takes 1 minute to make each cut?

Answer:

9 minutes.............the tenth piece falls off after the ninth cut.

DAY 92
It's true our sum is 60, and we differ just by 2. If you want to know our names, some thinking you must do.

Answer:

29 and 31

DAY 93
What letter comes next in this series?
J F M A M J J A S O N ___

Answer:

D............December

DAY 94
Subtract 24 from me, or take me from 42. Your answer is the same, whichever one you do.

Answer:

33

DAY 95
Together a doll and a dress cost $11. The doll cost $10 more than the dress. How much was the doll?

Answer:

$10.50

DAY 89
What is the next letter in this sequence?
S M T W T F __

Answer:

S..........Saturday

DAY 90
What number is as much below 50 as 4 times that number is above 50?

Answer:

20............50 - X = 4X - 50

DAY 91
Two men made a bet. The first man said, "I bet I can push something is a wheelbarrow for ten feet and you can't push it back." The second man was bigger and stronger, and he acceptd the challenge. What did the first man push in the wheelbarrow to win the bet?

Answer:

The second man

DAY 87
Can you find a number such that adding 4 to it, subtracting 4 from it, multiplying it by 4, and dividing it by 4, the resulting sum, difference, product, and qu0tient will add up to 150?

Answer:

24...........+ 4 = 28, - 4 = 20, times 4 = 96, divided by 4 = 6.

28 + 20 +96 +6 = 150.

(X +4) + (X - 4) + 4X + X/4 = 150.

DAY 88
What number when multiplied by 5 gives the same result as when it is added to 5?

Answer:

5/4 or 1.25 ............. 5X = X +5

DAY 85
One Yummy Drop weighs 5/8 oz. A box of Yummy Drops contains 12 1/2 oz. of candy. How many Yummy Drops are in a box?

Answer:

20

DAY 86
A textbook is opened at random. To what pages is it opened if the product of the facing page numbers is 3, 192?

Answer:

Pages 56 and 57...........X(X + 1) = 3192

DAY 83
Three students worked together washing and waxing Mr. Brown's car. Austin did 1/5 of the job, Beverly did 1/3 of the job, and Caroline's share of the money was $28. How much did it cost Mr. Brown to have his car washed and waxed?

Answer:

$60................Austin and Beverly did 8/15 of the job, so 7/15 X = $28

DAY 84
Two candles are lit at the same time. One is 12 inches tall and burns 1/2 inch per hour. The other is 6 inches tall and burns 1/4 inch per hour. Which candle will burn down first?

Answer:

They will burn down at the same time---in 24 hours.

Day 81
What is the next number and letter in this series?

3 T 4 Q 5 P ___ ___

Answer:

6 H..........6 Hexagon

DAY 82
Multiply this number by 1 1/3 or add 1 1/3 to this same number and the answer is the same. What is the number?

Answer:

4............4/3X = X + 4/3

DAY 79
A man born on December 27 celebrates his birthdat in the summer? Why?

Answer:

He lives in South America.

Day 80
Penny's parents have three children. One is named Nickel; one is named Dime. What is the name of the third child?

Answer:

Penny

DAY 76
Can you re-arrange the letters in TWELVE + ONE to get an equivalent statement?

Answer:

TWELVE + ONE = ELEVEN + TWO

Day 77
What are the next two terms in this series?
1 P 5 N 10 D 25 Q ___ ___

Answer:

50 H..........50 cents in a half-dollar

DAY 78
A rectangle 6 inches long and 3 inches wide has an area of 18 sq. inches and a perimeter of 18 inches. Can you think of another figure that has the same area as perimeter?

Hint: The area and perimeter are both 16.

Answer:

A square 4 inches by 4 inches

DAY 74
Rocky ate 1/3 of a bunch of grapes at lunch and 14 more after dinner. He ate the final 10 grapes while watching TV. How many grapes did Rocky have to start with?

Answers:

36 grapes

DAY 75
Which of these fractions is greater than 1/3 and less than 5/8?
2/9.....1/4.....2/3.....7/12

Answers:

7/12

DAY 72
Exactly how long does it take for sunlight to reach the earth, given that light travels at 186,000 miles per second and the sun is 93,000,000 miles from the earth.

Answers:

8 minutes and 20 seconds..........93,000,000/186,000 = 500 seconds = 8 1/3 minutes

DAY 73
If a month has Friday the 13th in it, on what day must the month begin?

Answer:

Sunday

DAY 70
3/7 of what number is 5/21

Answer:

5/9

DAY 71
In a field of cows, the difference between the number of ears and the number of legs is 40. How many cows are in the field?

Answer:

20..........the difference between ears and legs is 2 per cow. 40/2 = 20........or, since there are 1/2 as many ears as legs, the difference of 40 must be the number of ears.

DAY 68
1/2 your garden is planted in tomatoes, 1/4 of what is left is broccoli, 1/2 of what is left is lettuce, and the remainder is cauliflower. What fraction of your garden is cauliflower?

Answer:

3/16

DAY 69
What is 2/3 of 1/2 of 1/4 of 240?

Answer:

20

DAY 66
A man sells oranges for $.25 each. One day he sold 3/4 of his oranges, leaving him with 33. How much money did he make on the oranges he sold?

Answer:

$24.75.............33 must be 1/4 of the oranges he had to begin with. He sold 99 oranges (3/4 of 132).

DAY 67

1/2 is 1/3 of it. What is it?

Answer:

1 1/2............1/2 + 1/2 + 1/2 = 1 1/2

DAY 64
In a contest, you place both 13th highest and 13th lowest. How many people were in the contest?

Answer:

25 people..........12 higher than you and 12 lower than you.

DAY 65
How many trees need to be planted around a field 10 yards long and 6 yards wide, if there's one tree every yard?

Answer:

32 trees

DAY 62
You have $4.40 made up of the same number of nickels, dimes, and quarters. How many of each coin do you have?

Answer:

Eleven of each.............You can solve this using trial and error, but a more interesting appoach is to realize that one nickel, one dime, and one quarter add up to $.40. Since you have the same number of each type of coin, simply divide 4o into 440.

DAY 63
You win the lottery. You put 1/2 your money into college savings, 2/3 of the remainder is taxes, and there's $500 left. How much did you win?

Answer:

$3000.............After savings and taxes, 5/6 of the money is gone. 1/6 = $500.

DAY 60
You have 12 coins. 1/3 are dimes, 1/6 are quarters, 1/4 are nickels, and the rest are pennies. How much money do you have?

Answer:

$1.08..........4 dimes, 2 quarters, 3 nickels, 3 pennies

DAY 61
A squirrel finds 50 acorns in five days---three more each day than the day before. How many acorns did he find each day?


Answer:

4, 7, 10, 13, 16..........Let X = the number of acorns found on the first day. Then X+3 = the number of acorns found on the second day, etc. 5X+30 = 50

DAY 58
How much money is 10,000 nickels?

Answer:

1/20 of 10,000 = 500 dollars

DAY 59
If you were to build a square fort with six posts on each side, how many posts would you need?

Answer:

20..........The four corner posts can only be counted once.

DAY 56
If you drove to the beach averaging 60 mph and you returned the same distance averaging 40 mph, what would be your average speed?

Answer:

48 miles per hour.......The apparent answer--50 mph--is incorrect. Let's say the distance to the beach is 60 miles--120 miles round trip. (The answer is the same regardless of the distance.) Rate is determined by dividing distance by time. Traveling at 60 mph, it would take 60 minutes. Traveling at 40 mph, it would take 90 minutes. Total driving time is 150 minutes or 2 1/2 hours..... 120 = R(2.5) = 48 mph.

DAY 57
A bottle and a cork cost $1.10. The bottle costs 10 cents more than the cork. What is the cost of each?

Answer:

$.60 for the bottle and $.50 for the cork.........It's easy to say $1.00 for the bottle and $.10 for the cork. But this would be a difference of $.90, which does not satisfy the problem. Trial and error or algebra will give the correct answer [X + (X + 10) = 110], but a more interesting approach is to divide 110 in half--55--and then "split the difference" of 10 cents by going up 5 and down 5---giving 60 and 50.

DAY 54
There are 100 buidings along a street. A sign maker is hired to number the buildings from 1 to 100. How many "9's" will he need?

Answer:

20 nines (99 has two)

DAY 55
Find two positive numbers that have the same answer when added together as when multiplied together.

Answer:

2 and 2

DAY 52
Find two whole, positive numbers that have the same answer when multiplied together as when the larger is divided by the smaller. (Hint: There are a lot of them.)

Answer:

Any number and 1

DAY 53
How much do 10 pieces of candy cost if one thousand pieces cost $10.00?

Answer:

10 cents

DAY 50
Sam raced Jake in the 100-yard dash and beat him by 10 yards. The next day they raced again, but this time Sam started 10 yards behind the starting line. If both boys ran at the same speed as the previous day, who would win the race, or would it be a tie?

Answer:

Sam can run 100 yards in the time it takes Jake to run 90 yards. In the second race, the boys would be tied at the 90-yard mark. Since Sam is the faster runner, he would run the last 10 yards faster than Jake and win the race again.

Day 51
Which of the following letter designs is not like the other six?

Y E N F H A Z

Answer:

E is different because it is made of four straight lines. The others have three.

DAY 48
Eight dice are stacked on top of each other on a table. The die on top shows 1 dot. What is the total of all the numbers that are covered? You may not touch the dice. You may walk around the table if you want and look at the uncovered numbers, but you don't have to do this to solve the problem..

Answer:

The sides of a die that are opposite each other always equal 7. 7X7=49, which accounts for the first 7 dice. Now add the value of the bottom of the top die, which must be 6, giving a total of 55.

DAY 49
The ages of a father and a son add up to 55. The father's age is the son's age reversed. How old are they?

Answer:

The father is 41 and the son is 14.

DAY 46
Why would it take a plane flying from San Fracisco to New York nonstop longer than the same type of plane flying from New York to San Francisco nonstop, when weather, speed, winds, and all flying conditions were identical each way?

Answer:

The rotation of the earth from west to east would make the flight from San Francisco to New York longer.

DAY 47
Find two positive numbers that have a one-digit answer when multiplied and a two-digit answer when added.

Answer:

1 and 9

DAY 45

In a dish of red, green, and yellow M&M's, all but 2 are red, all but two are green, and all but two are yellow. How many M&M's are in the dish?

Answer:

3...........Let X = the number of M&M's in the dish

(X-2) = red, (X-2) = green and (X-2) = yellow
Adding........ 3X - 6 = X...........X =3 (one of each color)

DAY 43
Using only addition, make eight 8's equal 100.

Answer:

888 + 88 +8 +8 +8 = 100

DAY 44
A man can paint a room in four hours, and another man can paint the same room in 2 hours. How long would it take to paint the room if they worked together?

Answer:
80 minutes.....If X = total hours for the job, X/4 and X/2 represent the amount of work each man can do in one hour.........X/4 + X/2 = 1............ X = 4/3 hours.

DAY 42
Lily pads on a lake double in size every day so that they cover the entire lake in 10 days. On what day is the lake half-covered by the lily pads?

Answer:

Day 9

DAY 40
A man who drives 2 miles to work must average 30 mph to arrive on time. One morning heavy traffic cut his average speed to 15 mph for the first mile. What speed must he average in the second mile to arrive on time with a 30 mph average for the two miles?

Answer:

The man could not possibly make it to work on time. A trip of 2 miles at an average speed of 30 mph will take 4 minutes. The man averaged 15 mph for the first mile, which means that one mile alone took 4 minutes to drive.

DAY 41
A bicycle climbs a certain hill at 10 mph and returns at 20 mph. What is its average speed for the entire trip? (Credit: James F. Fixx in Solve It!)

Answer:

13 1/3 mph.....The apparent answer---15 mph---is wrong. Speed is determined by dividing distance by time. The answer is the same no matter what the distance.
Assuming the hill is 1 mile, 1 = 10T (going up) and 1 = 20T (going down). 1/10 of 60 = 6 minutes and 1/20 of 60 =3 minutes. So 2 = 9R or R = 2/9. 2/9 of 60 = 13 1/3 mph.

DAY 38
What number divided by four is the same as that number minus four?

Answer:

5 1/3........X/4 = X-4

DAY 39
If I give you $1, we'll each have the same amount of money. If you give me $1, I'll have twice as much as you. How much does each one of us have?

Answer:

I have $7 and you have $5.......If giving you $1 will make us even, I must have two dollars more than you. Let X = lesser amount and X + 2 = greater amount.
(X + 2) + 1 =2 (X - 1)

DAY 36
A common six-letter word changes into a number when you delete the first letter. What is the word and number?

Answer:

height/eight

DAY 37
What is the next letter in this sequence?

O T T F F S S E N __

Answer:

T.........as in TEN

DAY 34
If a standard-size cigarette can be rolled out of six standard-size cigarette butts, how many cigarettes can be made and smoked from 36 butts?

Answer:

7.....The 36 butts will yield 6 cigarettes, which when smoked, will yield 6 more butts. The 7th cigarette can be made from those 6 butts.

DAY 35
In the integers 0 to 99, which digit appears least frequently?

Answers:

O.....It appears only ten times. The other digits appear 20 times each.

DAY 33

As I was going to St. Ives,
I met a man with seven wives.
Each wife had seven sacks,
Each sack had seven cats.
Each cat had seven kits.
Kits, cats, sacks, wives,
How many were going to St. Ives?

Answers:

1.....all the others were coming from St. Ives. But how many were coming from St. Ives? 7 wives, 7 x 7 = 49 sacks, 49 x 7 = 343 cats, 343 x 7 = 2,401 kits:
7 + 49 + 343 + 2401 = 2,800.........+ the man........ = 2,801

DAY 31
A brick balances evenly with 3/4 of a pound and 3/4 of a brick. What is the weight of the whole brick?

Answer:

3 pounds.....If a brick weighs 3/4 of a brick plus 3/4 of a pound, the remainder of the brick (1/4) must weigh 3/4 of a pound. So 1/4 brick = 3/4 pound.

DAY 32
Teacher: Johnny, if you had six pieces of candy and I asked you for three, how many would you have left?

Answers:

Johnny: Six

DAY 29
Sixteen pingpong balls are placed inside a square, wooden rack in 4 rows of 4 so that they are held firmly together. How many additional balls are required to complete a pyramid on top of the 16-ball foundation? How many more would be needed to raise the pyramid one level higher?

Answer:

9 + 4 + 1 = 14
To raise the pyramid one level, 25 balls would have to be placed under the 16. Another level would require 36 balls---each new bottom level being a perfect square.

DAY 30
How many brothers and sisters are there in a family in which each boy has as many sisters as brothers, but each of the girls has twice as many brothers as sisters?

Answer:

4 brothers and 3 sisters.....If the boys have as many brothers as sisters, then there must be 1 more boy in the family than the number of girls. So the possiblilites are 2 boys and 1 girl, 3 boys and 2 girls, 4 boys and 3 girls and so on. 4 boys and 3 girls satisfies the reqirement that each girl has twice as many brothers as sisters.

DAY 27
In what popular sport does the lowest score win?

Answer:

golf

Day 28
A doctor gave his patient three pills at four o'clock and told him to take one every half-hour. The patient followed the doctor's instructions. At what time was he outof pills?

Answer:

five o'clock.....The patient takes the first pill at four o'clock.

DAY 25
A man was born in 50 B.C. and died on his birthday in 50 A.D. How old was he?

Answer:

99.....There is no year O.

Day 26
Use each of the digits 0-9 once to make them add up to 100. Begin with 89 +6 + 4

(Credit: James F. Fixx in Solve It!)

Answer:

89 + 6 + 4 + 1/2 + 35/70 = 100

DAY 23
In what three sports does the winner cross the finish line backwards? Two are recognized competitive events, while the third is an informal game-type activity. (Credit: James F. Fixx in Solve It!)

Answers:

rowing, backstroke, and tug-of-war

DAY 24
Ten people, all wearing hats, were walking along a street when a sudden wind blew all their hats off. A helpful boy retrieved them and without asking which hat belonged to which person, handed each person a hat. What is the probability that exactly nine of the people received their own hats?

Answers:

The probability is zero. If nine people have their own hats, then the tenth must too.

DAY 20
How much does a brick weigh if it weighs 5 pounds plus half its own weight?

Answer:

10 pounds

Day 21
A man is looking at a picture of a man. When asked who is pictured, the man replies: "Brothers and sisters have I none, but that man's father is my father's son." What relation is the man in the picture to the man looking at the picture?

Answer:

His son.....It's important that the man looking at the picture have no brothers, otherwise he might be looking at a picture of his nephew. That he has no sisters is a red herring.

DAY 22
A perfect number is one whose factors (excluding the number itself) add up to the number. 6 is a perfect number-----1+2+3 = 6. What is the next perfect number? (Hint: It's less than 30.)

Answer:

28..........1+2+4+7+14 = 28

DAY 19

A farmer has a fox, a duck, and a goose. He needs to ford a river and can carry only one thing with him as he crosses. If left alone, the fox will eat the goose, and the goose will eat the corn. How can the farmer safely get all three things across the river?

Answer:

The farmer takes the goose across first. He comes back and takes either the corn or the fox. He must then bring the goose back. He leaves the goose while he carries the corn or the fox across (whichever is left), then comes back for the goose.

DAY 17
How many one-inch cuts would it take to cut a 30-inch ribbon into 30 pieces?

Answer:

29---The 30th piece falls off after the 29th cut.

DAY 18
A logger has two identical logs. He cuts one log into four pieces in 36 seconds. How long will it take to cut the other log into five pieces?

Answer:

48 seconds---To cut the first log into four pieces requires only three cuts. So each cut takes 12 seconds. (Refer to Day 17 example.)

DAY 16

Two travelers stopped to eat. One had 5 loaves of bread and the other had 3. A third traveler arrived and asked to share their bread. They agreed and shared the bread equally among the three of them. The third traveler left $8 as payment. The traveler with 5 loaves felt he should get $5 and his friend $3---the same as their quantities of bread. The traveler with 3 loaves felt the $8 should be split $4 and $4, since the bread was shared equally. Unable to agree, they went to a judge, who correctly determined the fair distribution of the $8. What was the judge's decision?

$5-----$3
$4-----$4
$7-----$1

Answer:

$7-----$1..........Each man should be paid according to the amount over and above his own portion of the meal that he let the third traveler eat. Since the three men had shared the 8 loaves equally, each had eaten 8/3 loaves. Traveler one had 15/3 loaves, and traveler 2 had 9/3 loaves. Traveler 1 therefore gave away 7/3 loaves, while traveler 2 gave away 1/3 loaf. The ratio being 7:1.

Another way to solve: Since the third traveler paid $8, and the bread was shared equally, the value of the three loaves would be $24, or $3 per loaf. The first traveler contributed $15 and the second $9. Since each traveler ate $8 worth of bread (1/3 of $24), the first traveler should get $15 - 8 = $7 and the second traveler $9 - 8 = $1.

DAY 11
How many 9's are there between 1 and 100?

Answer:

twenty

Day 12
What unusual feature is shared by the numbers 1, 2, 3, 6, and 12?

Answer:

They add up to 24 and each is a factor of 24.

DAY 13
A man and his sister were walking together. The woman pointed across the street to a boy. "That's my nephew," she said. The man replied, "Well, he's not my nephew." If both were correct, how is this possible?

Answer:

The boy was the man's son.

DAY 14

Using a calculator, approximately how long is:

1,000 seconds

1,000,000 seconds

1,000,000,000 seconds

Answer:

1,000 seconds - 17 minutes

1,000,000 seconds - 12 days

1,000,000,000 seconds - 33 years

DAY 15

What is the next number in this sequence?

1/12...1/6...1/4...1/3...5/12...1/2...7/12...2/3...3/4...5/6..._____

Answer:

11/12.....The pattern is to add 1/12 to each term (and reduce).

DAY 6
A train one mile long, traveling 1 mile per minute, enters a tunnel 1 mile long. How long will it take the train to pass completely through the tunnel?

Answer:

2 minutes. After one minute, the train is completely inside the tunnel. It takes another minute for the train to get completely out of the tunnel.

DAY 7
What is the least number of horses that can satisfy this description? One horse in front of two horses, one horse between two horses, and one horse behind two horses.

Answer:

3

DAY 8
In the Rabbit Family there are 12 brothers. Each of the brothers has two sisters. How many children are in the Rabbit Family?

Answer:

14........... Each brother has the same two sisters.

DAY 9
A father and his son are in a car accident. Two ambulances come and the father and son are taken to different hospitals. The son needs surgery. When the doctor sees the boy, the doctor says, "I cannot operate on this boy. He is my son." How is this possible?

Answer:

The doctor is the boy's mother.

DAY 10
If 5 cats can catch 5 mice in 5 minutes, how long will it take one cat to catch one mouse? (Assume the cats are all of equal ability in catching mice.)

Answer:

5 minutes............ If 5 cats can catch 5 mice in 5 minutes, each cat is catching one mouse in 5 minutes.

This is a Problem-of-the-Day type blog designed for teachers grades 4 through 8 as an opening and/or closing activity to a classroom lesson. The problems involve computation as well as logical and critical thinking. In my own teaching experience, I have found that many of the problems can be expanded and lead to interesting discussions.

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DAY 1
A man has 10 white socks and 10 black socks in a drawer. They are single socks, not in pairs. The man gets up in the morning while it is still dark. He doesn't turn on the light and cannot see what colors the socks are. What is the least number of socks he must pull out of the drawer to be certain he has a matching pair - either black or white? What is the least number of socks he must pull out of the drawer to be certain he has a pair of each color?

Answer:

To be certain of getting a matching pair of either color, he must pull out 3 socks. He might have a pair after pulling out two, but to be certain, he must pull out 3. He must pull out 12 socks to be sure he has a pair of each color.

DAY 2
Two fathers and two sons were at a picnic. There were only three hamburgers. Yet each person at the picnic ate a whole hamburger. How was this possible.

Answer:

There were only three people at the picnic---a grandfather, a father, and a son. The father is both a father and a son.

DAY 3
A can with 40 mints in it weighed 135 grams. The same can with 20 mints weighed 75 grams. What is the weight of the can?

Answer:

15 grams

DAY 4
A man bought a parrot for $50, sold it for $60, bought it back for $70, and sold it again for $80. How much money, if any, did he make or lose?

Answer:

He makes $20. He makes $10 in each of two separate transactions. He does not lose any money when he buys the parrot back for $70.

DAY 5
How many ways are there to make change for a quarter?

Answer:

12---starting at two dimes and a nickel and ending with 25 pennies