A big thanks to all of our pizza loving math aficionados! We sent out the challenge and you answered in a big way. There were many correct answers but some typed faster than others. Winners have been notified via email, but we couldn’t bear to leave everyone hanging so answers are below!

OPTION A: I’m thinking of a ten-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is divisible by n for each n from 1 to 10. What is my number?

ANSWER: 3816547290 

OPTION B: Our school’s puzzle-club meets in one of the schoolrooms every Friday after school.

Last Friday, one of the members said, “I’ve hidden a list of numbers in this envelope that add up to the number of this room.” A girl said, “That’s obviously not enough information to determine the number of the room. If you told us the number of numbers in the envelope and their product, would that be enough to work them all out?”

He (after scribbling for some time): “No.” She (after scribbling for some more time): “well, at least I’ve worked out their product.”

What is the number of the school room we meet in?”

ANSWER: Room #12

The numbers in the envelope are either: 6222 or 4431, which both add up to 12 and the product is 48

• To truly get this right, you must first eliminate that #13 is NOT an option
• To do this you adjoin a 1 to the above numbers: 62221 or 44311, which both add to 13 and the product is 48
• And if you take 922 and 661, which both add to 13 the product is 36

OPTION C: My key-rings are metal circles of diameter about two inches. They are all linked together in a strange jumble, so that try as I might, I can’t tell any pair from any other pair.

However, I can tell some triple from other triples, even though I’ve never been able to distinguish left from right. What are the possible numbers of key-rings in this jumble?

ANSWER: Despite the internet’s best effort this one remains UNSOLVED! See below for a note from John H. Conway himself:

It reads: “If Any Solvers find this answer (which I’ve kept a closely guarded secret). I’ll look at their answers myself (there won’t be many perhaps even none).

Right again Professor Conway.