Vrijeme: 02:03

Ukrainski lanac | Ukraine chain #6

Jedna od drugih stvari koje Taras voli crtati su takozvani plus-shapes: unija pravokutnika 1 \times k s pravokutnikom m \times 1 (za neke k i m) koji se sijeku na jednom kvadratu koji nije krajnji lijevi/krajnji desni ili krajnji gornji/donji kvadrat za bilo koji od pravokutnika (tj. tako da dobiveni oblik nalikuje plusu, a ne slovu "T" ili "L" ili nečem drugom) . Plus-oblik ne mora biti simetričan. Na koliko načina može obojiti u žuto neka od polja na ploči 8 \times 8, tako da žuta polja formiraju plus?

Veliko hvala Arseniju Nikolaevu, osnivaču Quanta, koji je poslao ovaj lanac!

One of the other things Taras likes to draw are the so-called plus-shapes: a union of a rectangle 1 \times k with a rectangle m \times 1 (for some k and m) that intersect at one square which is not the leftmost/rightmost or uppermost/bottom square for any of the rectangles (i.e so that the resulting shape resembles a plus, and not a letter "T" or "L" or something else). A plus-shape does not have to be symmetric. In how many ways, can he colour yellow some of the squares on the board 8 \times 8, so that the yellow squares form a plus-shape?

Big thanks to Arsenii Nikolaev, founder of Quanta, who send this chain!