Logicians Numbers (Solution)

We will display A’s numbers on the left and B’s numbers on the right, like this:

• A: “Is your number double mine?”
• B: “I don’t know.”

Now we know that B’s number is even. If it was odd, he would say no.

• B: “Is your number double mine?”
• A: “I don’t know.”

Now we know that A’s number is even. If it was odd, he would say no.

Even more than that, we know that A’s number is a multiple of 4. It it was not, then A would know his number is not double an even number (and B’s number is even).

• A: “Is your number half mine?”
• B: “I don’t know.”

That rules out all the even numbers from 16 - 30 for B. He is left with 2, 4, 6, 8, 10, 12, 14.

• B: “Is your number half mine?”
• A: “I don’t know.”

That rules out all numbers above 7 since B’s highest possible number left is 14.

The only multiple of 4 less than 7 is 4. A’s number is 4.

• B: “I know your number.”