We have six statements about a number, and we know that exactly 1 is false.

1. I am greater than 50
2. I am a multiple of 7
3. I am a perfect square
4. I am a 3-digit number
5. I am less than 500
6. I am a multiple of 17

Are there any numbers that fit? How many? And if they exist, what are they?

Unrelated, interesting note: Nice factoring techniques for solving problems such as

Find n such that n(n+16) is a perfect square

are presented at the Ultimate Quant Marathon Blog for IIM Cat (whatever that means), a brand new blog. I think it’s called Quantologic for short.