Waow, impressive result, Fred -- many thanks! And to Hans also (private mail). I've just checked: S(max) = 1,4,44,2473,... is not in the OEIS. The solution for n=5 might arise from a search of what could be the best path -- regardless of any computations, having perhaps only patterns in mind (patterns of pathes)... My two (naïve) cents. Best, É. Le 14 avr. 2013 à 22:15, "Fred W. Helenius" <fredh@ix.netcom.com> a écrit :
On 4/14/2013 2:00 PM, Hans Havermann wrote:
Eric Angelini wrote:
My best MAX is 40: is it the highest possible MAX in a 3x3 square?
I believe the highest MAX is 44.
I concur with Hans, and add that the highest for a 4x4 square seems to be 2473 (barring software or hardware errors). The filled-in grid looks like this:
1 1 1239 2473
2 4 419 815
6 18 100 296
6 30 48 148
It's easy to figure out the order in which the numbers are entered. The two 6s are a bit surprising.
My brute force approach handles 3x3 in under a second and 4x4 in under two hours; 5x5 would seem to be infeasible without better ideas.
-- Fred W. Helenius fredh@ix.netcom.com
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