Question 167508: Hi, i've been having a lot of trouble slving this any help would be nice!
In order to join the math club at witless junior high, potential members must guess a secret whole number betwee 1 and 50, by asking yes-or-no questions only. Willy wanted to join so he tried the fowwing questions:
1. Is the number greater than 25?
2. is the number evenly divisible by 2?
3. is the number evenly divisible by 3?
4. is the number evenly divisible by 5?
After he was told the answers he found that he didn't have enough information.
he then asked the following question:
5. is the number a perfect square? Answer: No
what is the number?
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Ok, there are four questions, each yes or no. Which means each number can be classified into 1 of 16 groups. For example 42 is in the YYYN group (is >25, is div by 2, is div by 3, not div by 5). All of the numbers can be grouped this way.
Now we know that whichever group the number is in has more than one number, because we don't have enough information at this point. We also know that the number isn't a perfect square. So we need a group with more than one number in it, which when the perfect squares are removed only leaves one number.
After you list all the groups, you should find that the group NNNY has 2 members, 5 and 25. When we remove the perfect square (25) that leaves one member, 5, which is therefore the answer. You can also see that there are no other groups that work meaning 5 is the only answer.
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