Abel has 50, Bill has 20 and Clark has 30.
Abel on his first turn obviously doesn’t know whether his number is 50 or 10. Similarly neither Bill nor Clark can immediately figure out their numbers. However, on his second turn Abel can reason:
If mine is a 10, then Clark would know his number is either 10 or 30.
If it is 10, Bill would immediately know his number is 20. But he didn’t know.
So Clark should know his number is 30. Now since Clark didn’t know, my number must be 50.
If mine is a 10, then Clark would know his number is either 10 or 30.
If it is 10, Bill would immediately know his number is 20. But he didn’t know.
So Clark should know his number is 30. Now since Clark didn’t know, my number must be 50.
With this kind of reasoning we can also rule out all other combinations. So [50, 20, 30] is the only solution to this puzzle.
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