Mikey's Riddles topic

Edited by Dr Adequate, : No reason given.

Here's one I made up."I'm thinking of a number between one and ninety-nine," says Bob. "Guess what it is.""Give me a clue," says Alice. "What's the sum of its digits?" So Bob tells her."That's not enough information for me to figure out the answer," says Alice, "Is it greater than fifty?" So Bob tells her."Now I know what the number is," replies Alice. And tells him."OK," says Bob, "maybe that was too easy. I'm thinking of a different number between one and ninety-nine. Try again.""What's the sum of its digits?" Alice asks. So Bob tells her."Thank you," says Alice, "but that's not enough information to figure out the answer. Is it less than fifty?" So Bob tells her."In that case," says Alice, "I know your number." And she tells him what it is."OK, says Bob, "let's try again. I'm thinking of a third number between one and ninety-nine, different from the first two.""Is it greater than fifty?" asks Alice. So Bob tells her."And what's the sum of its digits?" asks Alice. So Bob tells her."Ah," says Alice, "now I know what your number is". And once more she is perfectly correct.So what (in the right order please) were Bob's three numbers?

Suppose the first number was 50. Then Bob's first two answers would have been "the sum of its digits is 5" and "no, it's not greater than 50". But in that case the possible numbers would have been 5, 14, 23, 32, 41 and 50, and so Alice wouldn't have known what the answer was.The key to solving it is the fact that Bob must be giving Alice enough information to deduce the numbers. The first number can't be 50 because in that case she wouldn't have enough information to deduce that that's what it was.

Not necessarily. If the time taken to make a move is proportional to the distance moved, then it would take an infinite number of moves but only a finite amount of time.

Whether or not infinity is a number it is clear that an infinite number of moves would in fact reach the door.Edited by Dr Adequate, : No reason given.