An excellent puzzle from JD2718:

There are five true and five false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number.

1a. I have 2 digits

1b. I am even

2a. I contain a “7”

2b. I am prime

3a. I am the product of two consecutive odd integers

3b. I am one more than a perfect square

4a. I am divisible by 11

4b. I am one more than a perfect cube

5a. I am a perfect square

5b. I have 3 digits

Please don’t post the solution in a comment, so as not to spoil it for others. But feel free to leave a comment if you need a hint, or to email me if you think you have solved it and want to check if you are correct. (Actually, it’s easy to check yourself: just make sure that each of each pair of statements, exactly one is true and one is false!)

## About Brent

Assistant Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.

It reminds me a bit of a puzzle I made. It is the top-right one on this page:

http://sites.google.com/site/jlnwebster/mathematics/puzzles-1

That was a great puzzle. Hard enough to make me think, not too hard to bore me. It requires a bit of deduction to solve.

Interestingly the site you link from says it is for kids, but I actually did use quite a bit of deduction.

Jack: neat puzzles, thanks for the link! And what, you think kids are not able to use deduction? =)

It took me an hour but I have done it maybe knowing cube numbers would of sped it up.

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Well, using matlab solving this took about 3 minutes. Basically I bounded it for 3 digit numbers and changed some variables around. Interesting puzzle! I might steal it for some students ;)

It took me about two minutes after I read all the clues, but I got lucky and guessed which clues I thought were right.

I wonder if there’s more than one answer.

robin: no, there is only one correct answer.

four of the five pairs of statements, you can tell definitively which applies. if there is a way to deduce which of the last pair applies without guess and check, i missed it. the good news is, the guess and check part goes as easily as you could possibly hope.

Fun puzzle, especially easy to check once you figure out which ones have to be true.

I got it after 20 minutes or so… but used excel to find the non-obvious pairings that didn’t work together. Once I worked out which clues *had* to be the true ones it was just a VLOOKUP to find the winner. YAY useless problem solving…