Wordy problem

[Guest]

The Maths teacher chooses a secret number and writes it on a price of paper.He tells the class that his number lies between 0 and 1000.He tells them he an find the answer in just 10 guess.How can I work this problem out?

[Guest]

always take the average

for example, the teacher chooses [tex]43[/tex]

first guess: [tex]\frac{1000}{2} = 500[/tex]

2nd guess: [tex]\frac{500}{2} = 250[/tex]

3rd guess: [tex]\frac{250}{2} = 125[/tex]

4th guess: [tex]\frac{125}{2} = 63[/tex]

5th guess: [tex]\frac{63}{2} = 32[/tex]

6th guess: [tex]\frac{32 + 63}{2} = 48[/tex]

7th guess: [tex]\frac{48 + 32}{2} = 40[/tex]

8th guess: [tex]\frac{40 + 48}{2} = 44[/tex]

9th guess: [tex]\frac{44 + 40}{2} = 42[/tex]

10th guess: [tex]\frac{42 + 44}{2} = 43[/tex]


-Jambo

[dantelentz]

thank you so much! only this helped me, too
steamdb

[HallsofIvy]

How does the teacher respond to your guesses? You take as a first guess "1000/2= 500". If the teacher simply responds "no, that is not the answer." There is no reason to take, as a second guess, "500/2= 250". The method of "bisection" used in the response assumes that the teacher responds "above" or "below". That was not implied in the original post!

[Guest]

In fact, why in the world would it take him 10 guesses to get the number he just wrote on a sheet of paper?