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.