Jedna od drugih stvari koje Taras voli crtati su takozvani
plus-shapes: unija pravokutnika
s pravokutnikom
(za neke
i
) 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
, 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
with a rectangle
(for some
and
) 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
, so that the yellow squares form a plus-shape?
Big thanks to Arsenii Nikolaev, founder of Quanta, who send this chain!
[lang = hr]
Jedna od drugih stvari koje Taras voli crtati su takozvani \textit{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?
\textit{Veliko hvala Arseniju Nikolaevu, osnivaču \href{https://www.quanta.world/}{Quanta}, koji je poslao ovaj lanac!}
[/lang]
[lang = en]
One of the other things Taras likes to draw are the so-called \textit{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?
\textit{Big thanks to Arsenii Nikolaev, founder of \href{https://www.quanta.world/}{Quanta}, who send this chain!}
[/lang]