Bob and Carol are each secretly assigned consecutive positive integers: they eac
ID: 2247822 • Letter: B
Question
Bob and Carol are each secretly assigned consecutive positive integers: they each know their own number and that the numbers are consecutive, but they do not know each other's number. They are told to sit in a room with a clock that chimes every hour. They cannot communicate in any way, but are told to wait in the room until they can deduce the other's number and then leave the room at the next chime of the clock. Prove by induction that the person with the smaller number, n, will leave the room after the nth strike of the clock.Explanation / Answer
As it is given that they are provided with positive consecutive numbers.
therefore, if one person is given 1 then for sure the other one would be given 2 (since 0 is not a positive integer).
Thus, now if one person is given 2 then as the first chime strikes if the other one has 1 will guess the number and game ends else he could not guess any number, which will clear the guess for first person that the second one has 3, and therefore the game will completes after 2 chime strikes.
Thus, similarly a person having n as a number, then he will wait till nth strike and if the other person guess the number which means that the second one has 'n-1' else the first one guess n+1.
And therefore if the smaller one is n, then they will correctly guess the numbers in n chimes.