Can you isolate a number, 1 through 10, by only asking 3 questions?

Question

for instance, i ask is the number greater than 5.. yes, is it greater than 7... yes, is it 8 or 9... yes... and thus 3 questions have been asked and it could still be 8 or 9.. so you need a fouth question to be 100% sure.. any trick to getting down to only 3 questions

yes you guys are right i should have specified yes or no questions... the greater than less than answer was good, and i liked the explanation of why it is impossible... however, it may just seem impossible at first, string together enough ands and ors in a yes or no question and you might find something so il keep this open for awhile

Answer 1

Yes, you just have to ask questions that are more informative than yes or no questions (for instance, the question "what is the number?" may isolate the number in one question). If you are limited to yes-or-no questions, however, then it is completely impossible, because there are only 8 different ways to answer a string of three yes-or-no questions (namely, NNN, NNY, NYN, NYY, YNN, YNY, YYN, YYY), and you can't distinguish between 10 numbers based on which one of only eight different sets of answers you receive.

Answer 2

< or > than 6, less
< or > than 3, greater
< than 5, no then the number is 5, yes then the number is 4

< or > than 6, greater
< or > than 8, greater, if less then number is 7
< than 10, no then the number is 10, yes then the number is 9


no answer means its the number the ? is about
your last ? is wrong is should be < or > than a number not an either or ?

Answer 3

I think so, the number is 6.
?1.Is the number odd or even? Even
?2.Is the number greater than 5? Yes
So now the number can only be 6,8 or 10.
?3. Is the number greater than 8? no
the number has to be 6 or 8....Crap never mind, almost had it.

Answer 4

well the only algorithm that works is to cut by half each time.
lets say 9
1. is the number greater, less than or equal to 5?
greater
2. is the number greater than, or equal to 7?
greater
3. is the number 8?
no
so there you go. Your number is 9 with only 3 questions asked.

Answer 5

Even with narrowing it down with three questions you can only have at most a 50% chance of guessing the number. So the answer is yes you could narrow it down but with only a 50% chance of actually guessing correctly, as you said you would need a fourth question to be 100% sure.

Answer 6

1.) Is it odd or even?
2.) Is it greater, less, or equal to 5/6 (depending on odd or even)?
3.) Is it divisible by 3 (if odd) or 4 (if even)?

Think that might work :)

Answer 7

its only possible if its an odd number

(possible 12345678910)

1. is it odd?
yes (possible 1359)

2. is it 1 or 3?

if yes ask,
is it 3?
if the answer is yes, you know its 3, if its no, you know its 2

if no ask,
is it 5?
if the answer is yes, you know its 5, if its no you know its 1

Answer 8

tell them to:
multiply the number by 2
add 2
divide by two
and then subtract it with the original number.

the answer will always be 1. :)