Puzzle: Who am I? (Teacher Edition)
[updated to correct a typo in b, and clarify d] [and d, again]
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?
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 not semiprime; ie, not 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 is a product of three primes, not necessarily distinct
d2: It is prime
e1: It is the sum of a square and a cube
e2: It is the sum of three squares
Please do not leave answers in the comments section! But do leave questions or discussion below.
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Source: I think Bertie Taylor from compuserve’s old SCIMAT forum. I don’t know where Bertie took his puzzles from. I posted it on this blog a few years ago, under the title Fallible Friends.
JD2718 
b2: do you mean “it does not have exactly two prime factors” or “it is semiprime”? They’re opposites, no?
Actually, no, I’m more confused than that even.
24 has exactly two prime factors: 2, and 3. But it is not semiprime.
If it is semiprime, it has exactly two prime factors.
If it has exactly two prime factors, it may be semiprime but need not be.
Which do you mean? (And, for d1, do you mean “it is pqr, with p,q,r prime”, or what you wrote? Or is it deliberately ambiguous?)
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