Mike Beeler <mikebeeler2@gmail.com> wrote:
Voted most favorite puzzle (24% of votes) was ?Factorials and Squares?: from the product 1! * 2! * 3! * ? * 100!, remove one ?term? K!, to make the result a perfect square. Attributed to Jeremy Kun.
I just brute-force solved it, but the unique solution gives me no insight. I suspect that there's a symmetry argument which I'm missing. I don't know how many decimal digits the product of all the factorials through 100 has, but the last 1124 of them are zeros. And the last 1112 digits of the perfect square are zeros. (Of course the latter must be an even number.) I reinvented A248663 in the process. Note that in the digest option of this list, all non-ASCII characters are turned into question marks.