## Sunday, November 29, 2009

### Number Logic

Jonathan, over at JD2718, has posted a logic puzzle he created, using lies and truths about numbers. I enjoyed it. But then our discussion turned to trying to create them.

I worked for a long time, starting from the answer I wanted and a bunch of things that were true and false about it. I couldn't get it narrowed down enough using just 5 clues. So I tried another number, and another. I think I've finally got a puzzle that works, but it doesn't feel as elegant as Jonathan's. Tell me if you get one possible answer. (But don't post the answer, please.)

And I'd love to know if anyone else has any success making these up.

Who am I?

There are four true and four 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 am the sum of two squares.
1b. I do not have any repeating digits.

2a. I'm even.
2b. I have exactly two digits.

3a. I'm prime.
3b. I am one less than a triangular number.

4a. I have just one digit.
4b. I am the product of consecutive primes.

1. Can you clarify (not sure that this question will matter):

Do 2 and 8 meet both 1a and 1b?

Jonathan

2. I guess they could. But if it said, "I am the sum of distinct squares", then they'd only satisfy 1b.

Let's go for modifying the wording, so they don't get knocked out by this clue.

Thanks!