This puzzle is a part of the Puzzling Stack Exchange Advent Calendar 2022. The accepted reply to this query will likely be awarded a bounty price 50 repute.
Have you ever questioned how Santa matches all of the presents in his bag? It’s easy – though the bag has finite dimensions on the skin, the within the truth is expands endlessly in all instructions, giving him infinite area to retailer all of the presents he must ship. To stop Santa from getting misplaced in infinite area, the slots for presents and filling materials have to be fastidiously organized in a repeatable sample. Slots for presents are all rectangular shapes (which have to be shaded within the grid), and every bit of filling materials have to be a non-rectangular form, lest Santa mistake it for a gift in his late evening cookies-and-milk-induced sugar rush. Two current slots can contact at a nook, however they can not share an edge; the identical applies for items of filling materials. Numbers within the grid point out the scale of the world (both current slot or piece of filling materials) containing the quantity. How ought to the contents of Santa’s bag be organised?
Oh, and no making infinitely massive presents or fillings! You don’t need to be the individual telling an overworked elf that he’ll be making an attempt to fill a single slot till subsequent Christmas. All areas within the completed grid (each shaded and unshaded) have to be of finite measurement.
TL;DR Nikoli’s Choco Banana in an infinite grid.
