# Puzzle – Who Am I? (Single statement pair deduction)

So that “Who Am I?” puzzle was fun. (Summary: there are a few pairs of statements about a number. Each pair contains one true and one false statement. Figure out what the number is)

Part of what made it so was the need to weave back and forth between the pairs. A major simplification would be to make deduction possible from some pair on its own.

For example, what if one pair said: I am a multiple of 3/I am even. Now we would know that the number should be even or a multiple of 3, but not both. Listing: 2, 3, 4, 8, 9, 10, 14, 15, 16,… A kid might express this strangely, but he will get it: the number is congruent to 2, 3 or 4 mod 6.

Another example: I am less than 10/I am less than 20. Since we need one true and one false, anything 20 and up fails (both false) and anything under 10 fails (both true!). Looks a lot to me like (x-10)(x-20) < 0. Neat.

Another: I am two digits/I am three digits. Just a simple idea to control the search.

Another: I am a multiple of 3/I am a multiple of 9.

So we might try:

1a. I am less than 45

1b. I am less than 16

2a. I am a 2-digit number

2b. I am a perfect square

3a. I am a multiple of 5

3b. I am a multiple of 10

Nice analysis. I didn’t do any of my clues that way on the one I just made. I think it’s still easier than the one you made.