With Christmas almost upon us, I thought I'd use this month's column to give you two of my favorite brain-teasers to challenge your relatives at that family gathering. What I like about these problems is that when you first meet them, you think you don't have enough information to solve them. But you do. You just have to look carefully at what the problem says. Both puzzles are about birds. I don't know the origin of the first one, but the second has a famous history.
"Of the birds that remained, a third were finches, a quarter were budgies, a fifth were canaries, a seventh were mynah birds, and a ninth were parrots."
However, the reporter got one of the fractions wrong. How many parrots were left?
A certain man buys 30 birds which are partridges, pigeons, and sparrows, for 30 denari. A partridge he buys for 3 denari, a pigeon for 2 denari, and 2 sparrows for 1 denaro, namely 1 sparrow for 1/2 denaro. It is sought how many birds he buys of each kind.
As before, what makes this problem particularly intriguing is that it seems you don't have enough information to solve it. Specifically, it looks like you have two equations in three unknowns. In fact, in terms of equations, that is precisely what you do have. But the problem gives you additional information that turns out to be all you need to find the (unique) answer.
I'll give the answers to both puzzles in next month's column.
Devlin's Angle is updated at the beginning of each month. Find more columns here.