## Recreational Math## Math Puzzles |

## What is an example of a logic puzzle? |

Most of us have encountered logic puzzles before, usually on mathematics tests given in grade and high school. They often contain numbers (the mathematics connection) and a (often seemingly convoluted) sequence of events to which the reader has to determine the outcome.

For example, the following will jar the memory banks of everyone who has ever seen such logic puzzles on an exam or elsewhere: One weekend, three people check into a bed and breakfast. They pay $30 ($10 each) to the B&B owner and go to their room. The owner remembers that there is a special deal that weekend, and the actual room rates come to $25. He gives $5 to his brother (who works with him) and tells him to return the money to the guests. On the way to the room, the brother realizes that $5 would be difficult to share between three people—5/3 = 1.666 …, an uneven number—so he pockets $2 and gives $1 to each person. Therefore, each person paid $10 and got back $1; this means they paid $9 each, totaling $27. The brother has $2, so the entire total is $29. Where is the remaining dollar?

The solution? Deduction comes in handy here. It’s the owner who’s important to pay attention to, not the brother. Overall, each guest paid $9 (a total of $27), the owner now has $25, and the brother has $2; thus, the brother’s amount should be either added to the owner’s money (25 [owner] + 2 [brother] + 3 [guests] = 30), or subtracted from the guests’ amount of $27 (27 [guests] -2 [brother] + 5 [refund from owner] = 30)—not added to the guests’ amount. This proves that not only is the owner’s brother a bit dishonest, but also how easy it is to con some people out of a few dollars if they aren’t used to solving logic puzzles!