Selected Puzzles



Q:

Three wise men are lined up in single file, each wearing a white hat. They know there were 5 hats total, three white, and two black, but they can only see the hats on the men in front of them. They don't speak unless they figure out what color hat they have on. Who figures out first?


A: Assume they are looking left in the order A,B,C. If C saw two black hats he would know he had white. If B saw one black and C didn't say anything, he would know he had white. But neither C nor B say anything, so then A knows he must have white.
.

Q:

A father and his son are in a car crash. The father is killed instantly but the son is only injured and is taken to the hospital. He is rushed to the operating room, the doctor comes in, looks at the patient on the operating table, and says, "I can't operate on him, he's my son." How can this be?


A: The doctor is the mother of the patient
 

Q:

A farmer has a 40 lb stone that he uses to measure out bales of hay on a 2 sided balance. He loans it to a friend who accidentally breaks it into 4 pieces. Instead of being angry, the farmer is quite happy. He says to the friend, "you managed to break it into just the right 4 pieces that will now let me weigh any weight between 1 and 40." What are the weights of the 4 pieces?


A: 1, 3, 9, and 27.
You can put multiple pieces on the scale to add their weights, or put pieces on the other side to subtract them.
 
 

Q:

You have 2 bowling balls that each breaks when dropped from the same height. You want to find the highest floor of a 10 story building from which these balls can be dropped without breaking. Devise an optimal procedure that can always locate that floor using not more than N drop tests. What is the smallest N can be?


A: 4
With 1 drop you can test 1 floor. With 2 drop you can test 3 floors: Test the 2nd floor first. It it breaks,test the bottom floor with the other ball. If not, test the top floor with either ball. With 3 drop you can test 6 floors: Test the 3rd floor first. If it breaks test the bottom 2 floors in order with the other ball. If not, test the top 3 floors as described above. With 4 drop you can test 10 floors: Test the 4th floor first. If it breaks test the bottom 3 floors in order with the other ball. If not, test the top 6 floors as described above.
 


Selected Puzzles