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