Marinada '26

[lang=hr] Cijeli brojevi od 1 do 64 smješteni su u nekom poretku u mrežu ćelija dimenzija $8\times8$, pri čemu se u svakoj ćeliji nalazi po jedan broj. Neka je $a_{i,j}$ broj smješten u ćeliju u $i$-tom redu i $j$-tom stupcu, i neka je $M$ zbroj apsolutnih razlika između susjednih ćelija. Odnosno, $$M = \sum_{i=1}^8 \sum_{j=1}^7 (|a_{i, j+1} - a_{i, j}| + |a_{j+1, i} - a_{j, i}|).$$ Koja je najveća moguća vrijednost $M$? [/lang] [lang=en] The integers from $1$ to $64$ are arranged in some order in an $8\times 8$ grid, with one number in each cell. Let $a_{i,j}$ denote the number placed in the cell in the $i$-th row and $j$-th column, and let $M$ be the sum of the absolute differences between numbers in adjacent cells. That is, $$ M = \sum_{i=1}^{8} \sum_{j=1}^{7} \left( |a_{i,j+1} - a_{i,j}| + |a_{j+1,i} - a_{j,i}| \right). $$ What is the greatest possible value of $M$? [/lang]