So I gave a three digit number to five of my friends and they all told me two facts about it. Unhappily each person gave me one correct fact and one incorrect fact. What was the number?

A challenge for all is in the discussion, below the fold

a1: It is the difference between two squares
a2: It is not the sum of two cubes

b1: It is an even number
b2: It does not have exactly two prime factors (it is semiprime; ie, of the form a*b where a and b are both prime)

c1: It is the sum of two squares
c2: It is both a square and a cube

d1: It has exactly three prime factors
d2: It is prime

e1: It is the sum of a square and a cube
e2: It is the sum of three squares

For discussion, enter a comment below. For solutions, click the solutions page.

Whether or not you solve this, here’s a challenge that’s worth trying. Can you create one of these of your own? Use two, or three fallible friends, to make it easier. Restrict it to two digit numbers, if that helps. Writing these is not easy, but kids eat them up. Click here to post answers to the challenge.

Source: I think Bertie Taylor from compuserve’s old SCIMAT forum. I don’t know where Bertie took his puzzles from.