Consecutive numbers on two foreheads

Question

Rex and Sol each get a positive whole number stuck to their forehead. They're told the two numbers are consecutive, they differ by exactly 1 (like 6 and 7). Each can see the other's number but not their own. Every round, both are asked at the same time, "Do you know your own number?" and answer honestly. Here's what happens: - Round 1, Rex: "No." Sol: "No." - Round 2, Rex: "No." Sol: "No." - Round 3, Rex: "No." Sol: "Yes, I know mine!" What number is on each forehead?

Accepted Answer

The key fact: since the numbers are consecutive positive whole numbers, whoever sees a 1 instantly knows their own number is 2 (it can't be 0). Watch how each "No" pushes the possible numbers higher. After Round 1 (both say No): Neither person sees a 1, otherwise that person would have answered "yes." So neither number is 1; both are at least 2. After Round 2 (both say No): Now consider a player who sees a 2. Their own number is 1 or 3, but 1 was just ruled out, so they'd know it's 3. Since both still say "No," neither person sees a 2, which means neither number is 2; both are at least 3. Rou…

Consecutive numbers on two foreheads

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