Like the famed "Parker Square", but with distinct digits. Examples exist for 4x4, 5x5, 6x6, maybe higher. 3x3 is conjectured impossible. It must be a square of distinct perfect square integers such that each row, column, and diagonal sums to the same number.
Inspired by https://www.youtube.com/watch?v=U9dtpycbFSY, where the latest Numberphile guest conjectures this is the case.
See also
General policy for my markets: In the rare event of a conflict between my resolution criteria and the agreed-upon common-sense spirit of the market, I may resolve it according to the market's spirit or N/A, probably after discussion.
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@Conflux If I prove this and post a pdf of it in the comments, does that count? What is the standard of rigor needed here?
See this webpage from 2005. Between the explicit examples for n=4,5,6,7 there and the article he references, which claims (pg 58)
Bimagic squares of size 8x8 and above are already known
it seems like this is proven.
@BoltonBailey oh huh, I think you’re right. I’ll try to find time to look closer soon but I think this is a yes
@Conflux I hadn't seen it until you mentioned it, but yes the video and this paper referenced in it explicitly claims it (although again, seems like this was known 20 years ago).
@BoltonBailey Yeah, this is just already proven. A little silly of me to make the market then, but seems like a yes!
@Conflux Well, not very silly, since it seem like the mathematician in that earlier numberphile video didn't realize either!