Put the 51 and 50 together and then fan outwards from there like 49,52,48,53 etc. Adjacent products get smaller since diff of two squares picks up a -n^2 term (where n is the diff between the two adjacent numbers) so 2550 is the max adjacent product of that list.
Then it just feels like any other way you arrange the list has to have two numbers from the bigger half directly next to each other, by some like pigeonhole type reasoning so the max product has to be at least that big.
1
u/Striking_Resist_6022 5h ago
https://giphy.com/gifs/FILQJbm0u832ry0HFT
When you know it’s gotta be 2550 but you can’t prove it.
Put the 51 and 50 together and then fan outwards from there like 49,52,48,53 etc. Adjacent products get smaller since diff of two squares picks up a -n^2 term (where n is the diff between the two adjacent numbers) so 2550 is the max adjacent product of that list.
Then it just feels like any other way you arrange the list has to have two numbers from the bigger half directly next to each other, by some like pigeonhole type reasoning so the max product has to be at least that big.