SOLUTION: 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 numb

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.
RELATED QUESTIONS
You ride your bike up a steep mountain road at 5 miles per hour. How far do you go in 3... (answered by Alan3354)

Hi, I am having such trouble with these equations. My book goes over one example in which (answered by richwmiller)

Hello I'm having trouble setting this problem up. Any help would be appreciated. Thanks. (answered by ikleyn,josgarithmetic,MathTherapy)

This is a different kind of question any advice would be appreciated. I�m planning to go... (answered by stanbon,ikleyn)

I subscribe to the Comic-of-the-Month Club. Each month I can buy any number of the 48... (answered by josmiceli,richwmiller)

Hi all, I am having some trouble with vectors at the moment, I was hoping someone could... (answered by Alan3354)

Having a lot of trouble with this. Please help and show me how so I can actually learn... (answered by stanbon)

Hi, There's a word problem on vectors that I've been having trouble with: "What... (answered by htmentor)

For such an easy looking problem I seem to be having a lot of trouble with it I need to... (answered by Fombitz)