Pizza Dividends (July 2025 Challenge Question)

When each sister starts her process she must have multiple of four slices.

The younger sister can't start with eight slices because it wouldn't leave enough slices for the other two sisters to have more. It's fair to assume she doesn't start with zero slices but in fact if you do work through that scenario you can show that it's impossible.

So it's clear that the younger sister starts with four slices. She gives one each to her older sisters and it's now easy to see that the middle sister must have started with seven. That leaves 13 for the older sister and when she receives one from her younger sister and two from the middle sister she has 16 which means she can keep eight for herself and give four each to the other two sisters.

The sisters are 7, 10 and 16

As is common, this puzzle is easier to solve in reverse. The final state is [8 8 8]. The sharing algorithm is to give away half of your pizzas to the other two (1/4 each). Solving in reverse, the unsharing algorithm is to take from the other two sisters your total number (1/2 from each). Let A be the youngest sister, B the middle, and C the oldest.

A B C

8 8 8 (final state)

4 4 16 (C unshares)

2 8 14 (B unshares)

4 7 13 (A unshares = their ages 3 years ago)

7 10 16 (Their ages today)