Here's another number guessing game:
I randomly pick a number from 1 to 1000. After you make your first guess at the number I will only tell you whether it is warmer (closer) or cooler (farther) or neither, to a 'zero^{th} guess' of 500.
For successive guesses I will tell your warmer, colder, neither, to the closest of the previous guesses.
What is the minimum number of guesses that would guarantee that you win with an optimal strategy?
What is this strategy?
(In reply to
How does the game end? by Steve Herman)
You win when you guess the number.
If your first guess is 600 and the number is 600 then you win in 1 guess.
If your first guess is 600 and I say "neither" you will win in two guesses, since you know the number is 550.
If your first guess is 600 and I say "warmer" you know it is above 550 (but not 600.)
If your first guess is 600 and I say "colder" you know it is below 550 (but not 500.)

Posted by Jer
on 20131002 13:09:12 