If I think of a number between 1 and 1,000, guessing it in 10 yes-no questions is easy... so that's not the puzzle!

Guessing it in 10 yes-no questions, that must be all asked in advance, is also relatively easy... so that's not the puzzle either!

How many questions would you need to guess my number, if you had to ask all questions beforehand, and I also could lie once?

There are 1024 distinct possible answers when asking 10 questions, but if you are allowed to lie once, then it means that each number must have 11 combinations of answers which are corresponding uniquely to it - because there is one combination of answers in case all are true, and one more combination for each question that can be answered as a lie... for example, if a certain number would lead to the answer combination:

no no no no no no no no no no

then it should also be uniquely accepted by

yes no no no no ...

no yes no no no ...

etc...

and thus we need a number of question such that its corresponding power of 2 is greater than 11000....

Posted by ronen on 2005-04-15 08:35:42