July 2017
Problem of the Month
The Game Devisers
It was a slow day at the cafe when Eliza and Anna came up with a game to play. Anna said,
"I'll think of a positive number of 75 or less.
Ask me yes-or-no questions and see how quickly you can guess the number."
Eliza, who had never been known to ask an irrelevant question, plunged in thusly:
1. Is it a prime number?
2. Is it divisible by 2?
3. Is it divisible by 3?
4. Is it divisible by 5?
5. Is it less than 25?
The questions are given in the order Eliza asked them. After the fifth question was answered — and not before — Eliza had figured out Anna's number.
Can you determine the number and the answers that Anna gave to the five questions?