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.
Wednesday 30 September 2009
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
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
Tuesday 29 September 2009
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:
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:
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:
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 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
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
Monday 28 September 2009
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
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:
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 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
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.
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.
Sunday 27 September 2009
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?
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.
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.
Saturday 26 September 2009
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................
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................
Friday 25 September 2009
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.
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
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
Thursday 24 September 2009
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
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
Wednesday 23 September 2009
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.
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:
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 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.
Saturday 19 September 2009
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:
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:
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?
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.
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 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
Thursday 17 September 2009
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.
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 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:
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?
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:
Answer:
A square 4 inches by 4 inches
Saturday 12 September 2009
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:
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.
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.
Friday 11 September 2009
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?
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:
$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
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.
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:
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 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
Thursday 10 September 2009
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.
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 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
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.
Wednesday 9 September 2009
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.
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
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
Saturday 5 September 2009
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:
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)
Adding........ 3X - 6 = X...........X =3 (one of each color)
Friday 4 September 2009
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.
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.
Thursday 3 September 2009
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.
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)
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)
Wednesday 2 September 2009
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.
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
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
Tuesday 1 September 2009
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:
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:
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.
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.
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.
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