3 items are filed under this topic.








A key for a lock with five tumblers 
20161102 

From Aeriel: A lock works by having a key turn a sequence of tumblers. Consecutive tumblers have different heights, and in order to unlock the lock, the sequence of heights on the key must exactly match those of the lock. The picture below shows a lock with four tumblers.
How many different keys can be made for a lock that has 7 tumblers with 5 possible heights each? Answered by Penny Nom. 





Coconuts and Monkeys 
20060508 

From Meadow: 5 sailors plan to divide a pile of coconuts among themselves in the morning. During the night, one of them decides to take his share. After throwing a coconut to a monkey to make the division come out even he takes 1/5 of the pile. The other four sailors repeat this procedure, each throwing a coconut to the monkey and taking 1/5 of the remaining coconuts. In the morning the 5 sailors throw a coconut to the monkey, and divide the remaining coconuts into 5 equal piles. What is the minimum number of coconuts that could have been in the pile originally? Answered by Paul Betts. 





Three keys 
19981126 

From Karen Chan: A man has a bunch of three keys, only one of which fits the lock of his front door. When he comes home in the dark he tries the keys at random until he finds the one fits. Find the probability that in a week of five nights, he tries the right key first on at least one night. Answered by Penny Nom. 


