For this month’s puzzle, solvers were tasked with picking three distinct positive integers that could support not one but two corner-to-corner knight’s journeys on a 6-by-6 board, each scoring exactly 2024 points.

Nearly 40% of the entries we received managed to achieve a minimal sum of A + B + C = 6. Since C needed to be a divisor of 2024, this meant there were only 4 plausible permutations:

• (1, 3, 2) [the most popular set of values across all entries, appearing 214 times]
• (3, 2, 1) [the next most popular, appearing 86 times]
• (3, 1, 2) [third-most popular; 54 times]
• (2, 3, 1) [sixth-most popular¹; 31 times]

Of the many entries we received, we would like to highlight a few:

• The longest journeys – for both the a1-to-f6 leg and for a6-to-f1 – came from Fred Vu, who chose (3, 1, 2) and supported it with the 32-move a1,c2,a3,b1,d2,f3,e1,d3,b2,a4,c5,a6,b4,a2,c1,b3,a5,c4,e5,c6,d4,b5,d6,f5,e3,d5,f4,e2,c3,d1,f2,e4,f6 and the theoretically-maximal 34-move a6,c5,d3,e1,f3,e5,c6,a5,b3,a1,c2,a3,b1,d2,c4,b6,a4,b2,d1,f2,e4,f6,d5,f4,e6,d4,e2,c1,a2,c3,b5,d6,f5,e3,f1.

• The journey with the largest number of “multiply” moves (16) came from Justin Snopek, who also chose (3, 1, 2) and whose a6-to-f1 path went a6,c5,a4,c3,a2,c1,e2,f4,d5,b6,c4,e5,d3,f2,d1,e3,f5,d4,f3,d2,f1.

• Of the many entries we received that achieved the theoretical lower bound of 12 total moves (6 for each journey), the lowest value for A + B + C we received was 19. The first entry we received to accomplish this came from Shyam Padmanabhan, who picked (4, 7, 8) and supported it with the journeys a1,b3,d4,c6,b4,d5,f6 and a6,b4,c6,d4,c2,e3,f1.

• There were a handful of triples (A, B, C) that we received exactly once. The one with the lowest sum was (2, 1, 4), courtesy of Richard Turner; its accompanying trips were a1,b3,d2,f1,e3,d5,f4,e2,c3,a2,b4,c2,e1,d3,f2,d1,b2,c4,d6,e4,f6 and a6,c5,e4,f2,d1,c3,b5,a3,c2,d4,c6,b4,d5,f4,e2,c1,b3,d2,f1.

Of the nine plausible values for C – i.e. divisors of 2024 no larger than 47 – the most popular among entries was 2, appearing in 335 entries. After that, the most popular were 4 (167 entries), 8 (153), 1 (126), 22 (99), 11 (84), 23 (17), 44 (4) and 46 (2). (46 was also the largest integer to occur in any entry, appearing in just those 2.)

And finally, the least positive integer to appear in exactly zero entries was… 19.

Congrats to everyone who sent us a valid entry!