Logic Riddles

 
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Question: Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.

Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.

What are the numbers?

Answer: The numbers are 3 and 4.

Since Sam knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Pete (who knows x*y) knew that Sam didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Pete doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2). At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.

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Question: A semi truck weighing exactly 10,000 pounds gets onto a bridge that is 100 miles long. The bridge's weight limit is exactly 10,000 pounds, any more will break the bridge. After going about 80 miles down the bridge a small bird lands on the truck.

What happens?

Answer: Nothing, after traveling 80 miles the truck will have surely burnt enough fuel to allow the bird to land on the truck without breaking the bridge.

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Question: You have been given the task of transporting 3,000 apples 1,000 miles from Appleland to Bananaville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Bananaville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Appleland).

What is highest number of apples you can get to Bananaville?

Answer: 833 apples.

Step one: First you want to make 3 trips of 1,000 apples 333 miles. You will be left with 2,001 apples and 667 miles to go.
Step two: Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).
Step three: Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Bananaville.

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Question: There are 3 men, two Chimps, and one Gorilla on one side of a river:

  • They have a boat but only the men and the Gorilla can row the boat across, so there must always be a human and/or Gorilla on the boat.
  • The boat can only carry two people/monkeys.
  • If monkeys and humans are together on one side of the river there must be as many or more people than monkeys for the men's safety.
How can all men and monkeys make it to the other side?

Answer: Steps: (They all start on the left side).
(Left side | Right side)

(3 men, 1 Gorilla, 2 Chimps | 0 men, 0 Gorilla, 0 Chimps)
-> Chimp and Gorilla (3 men, 0 Gorilla, 1 Chimps | 0 men, 1 Gorilla, 1 Chimps)
<- Gorilla (3 men, 1 Gorilla, 1 Chimps | 0 men, 0 Gorilla, 1 Chimps)
-> Chimp and Gorilla (3 men, 0 Gorilla, 0 Chimps | 0 men, 1 Gorilla, 2 Chimps)
<- Gorilla (3 men, 1 Gorilla, 0 Chimps | 0 men, 0 Gorilla, 2 Chimps)
-> Two men (1 men, 1 Gorilla, 0 Chimps | 2 men, 0 Gorilla, 2 Chimps)
<- Human and Chimp (2 men, 1 Gorilla, 1 Chimps | 1 men, 0 Gorilla, 1 Chimps)
-> Human and Gorilla (1 men, 0 Gorilla, 1 Chimps | 2 men, 1 Gorilla, 1 Chimps)
<- Human and Chimp (2 men, 0 Gorilla, 2 Chimps | 1 men, 1 Gorilla, 0 Chimps)
-> 2 men (0 men, 0 Gorilla, 2 Chimps | 3 men, 1 Gorilla, 0 Chimps)
<- Gorilla (0 men, 1 Gorilla, 2 Chimps | 3 men, 0 Gorilla, 0 Chimps)
-> Gorilla and Chimp (0 men, 0 Gorilla, 1 Chimps | 3 men, 1 Gorilla, 1 Chimps)
<- Gorilla (0 men, 1 Gorilla, 1 Chimps | 3 men, 0 Gorilla, 1 Chimps)
-> Gorilla and Chimp (0 men, 0 Gorilla, 0 Chimps | 3 men, 1 Gorilla, 2 Chimps)

And they are all safely across.

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Question: There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.

How much water evaporated?

Answer: 50 pounds.

In the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.

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