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How Old is Malcolm, His Dad and Grandfather?

Malcolm is the number of weeks of his father’s age treated as days and his grandfather’s age in months. All three of their ages add up to 120 years. How old is Malcolm, his father and his grandfather?

Malcolm is 6.
The father is 42. 42 days = 6 weeks.
The grandfather is 72. 72 months = 6 years.

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The Japanese IQ Test

Supposedly this is given as a test in Japan. I have no idea if that’s accurate.

There are 8 people who have to cross the river on a raft.

1. Policeman
2. Thief
3. Father
4. Boy 1
5. Boy 2
6. Mother
7. Girl 1
8. Girl 2

The rules are:

Only two people can cross at a time.
Only the adults can operate the raft.
The father can’t be with the girls unless the mother is there.
The mother can’t be with the boys unless the father is there.
The thief can’t remain with anyone unless the policeman is present.

How do you get them all across?

Instead of working it out by hand, here’s a flash version.

Click on the circle to start. Click on a person to put them on the raft and click on the lever to make the raft cross.

Here’s how I did it in 17 steps. Can you do it faster? Let me know in the comments.

1. Policeman (P)
2. Thief (T)
3. Father (F)
4. Boy 1 (B1)
5. Boy 2 (B2)
6. Mother (M)
7. Girl 1 (G1)
8. Girl 2 (G2)

1. P, T →
2. ← P

3. P, B1 →
4. ← P T

5. F, B2 →
6. ← F

7. F, M →
8. ← M

9. P, T →
10. ← F

11. M, F →
12. ← M

13. M, G1 →
14. ← P T

15. P, G2 →
16. ← P

17. P, T →

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Four Colored Balls in Gym Class

Four different-colored balls are being used in a gym class activity – blue, red, yellow and orange. Each student must hold two different-colored balls, but no two students can have the same two colors (for example, only one student can hold the blue and red ball).

How many students can play the game?

Six. If you prefer math, you can calculate it as 4 combination 2

4! / (2!)^2
24 / 4 = 6

Or you can work it out manually:

1. Blue Red
2. Blue Yellow
3. Blue Orange
4. Red Yellow
5. Red Orange
6. Yellow Orange

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Planting Trees on Arbor Day

On Arbor Day the fourth grade class began planting trees. They finished planting five trees before the fifth grade class arrived. But they accidentally planted them on the fifth grade side of the street.

The fourth-graders crossed the street to start over, and the fifth-graders planted the remaining trees. They finished first and felt bad for the fourth-graders, so they crossed the street and planted five trees. They planted another five trees at which point all of the trees had been planted.

By how many trees were the fifth-graders ahead of the fourth-graders?

Ten. The fifth-graders planted five more trees than they were assigned, and the fourth-graders planted five fewer than their assignment.

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Sunny Weather Coming?

It’s raining at midnight. Will there be sunny weather in 72 hours?

No, because in 72 hours it will be midnight again.

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Three Kinds of Apples

Three kinds of apples are mixed randomly in a box. How many apples must you take out to be sure of having at least two apples of one kind?

Four. If the apples are A, B, and C, it’s possible that you could take out one A, one B and one C with three apples, but the fourth apple must be one of the three kinds.

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Three Philosophers Under a Tree

Three philosophers are taking a nap under a tree. While they’re asleep, a small boy smears their noses with red berries. When they awake, they each begin to laugh, thinking the other two are laughing at each other.

But then one philosopher stops laughing, realizing his nose is red too. How did he come to this conclusion?

Let’s call the philosopher’s A, B and C. A reasoned that B was confident his nose wasn’t red. If B saw A’s nose wasn’t red, he would be surprised that C was laughing, because C would have nothing to laugh at. But B wasn’t surprised, therefore, A correctly reasoned his nose was smeared.

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The Horse and the Plane

A delivery truck from the post office is sent to the airport to meet a cargo plane. The plane lands ahead of schedule, and its contents are brought toward the post office by car. After a half hour, the car meets the truck and they exchange the contents.

The truck returns from the post office 20 minutes early. How early did the plane arrive?

The delivery truck arrived back 20 minutes early, so it would have taken 20 minutes to go from where it met the car to get to the airport and back. Therefore, the car and truck met 10 minutes from the airport. Adding those 10 minutes to the 30 minutes the truck had already driven to meet the car means the plane arrived 40 minutes ahead of schedule.

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Kaitlyn’s Age Plus and Minus Three

Kaitlyn’s age plus three has an integer square root. Three years ago, Kaitlyn’s age was the square root.

How old is Kaitlyn?

Kaitlyn is 6 years old.

6 + 3 = 9, and 9 has an integer square root.

6 – 3 = 3, and 3 is the square root of 9.

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