Stolen Root Beer
Published in Brain Teasers
Fred, who owns a restaurant, is convinced that one of his employees is stealing root beer from him. Since he is a bad businessman, he doesn't keep very good records of his inventory or his employees, so he doesn't know who is doing it. He decides to set a trap to find out who is stealing from him.
He assigns each of his employees a different night to close up shop. He then arranges the last 28 bottles of root beer in a square so that each side has nine bottles, as shown below:
2 5 2
5 0 5
2 5 2
Fred figures that whatever day he comes in where there are no longer nine bottles to a side, he will know it was the person who closed the night before who is doing it.
Unfortunately for Fred, Bob, the thief, figures it out and manages to take four more bottles the night of his shift, rearranging the bottles so that Fred doesn't realize they're missing. Not only that, but Bob was able to take four more bottles away the next night he closed while still rearranging them to have nine bottles on each side.
How did Bob do it?
Solution:
After Bob takes the first four bottles, he arranges the remaining 24 bottles like this:
3 3 3
3 0 3
3 3 3
When he takes the next four and only leaves 20 bottles, he arranges them like this:
4 1 4
1 0 1
4 1 4
Today's brain teaser courtesy of Braingle.com.
