Question 21
Nacho must write the $26^2=676$ integers from 1 to 676 on a $26 \times 26$ board, one in each box. Next, Julian chooses two neighboring squares (with a common side or vertex). Julián's objective is for the sum of the numbers in those two boxes to be a multiple of 4. Determine if Nacho can distribute the numbers so that it is impossible for Julián to meet his objective.