Folkpor

A square $4 \times 4$ is called magic if its cells contain all numbers from 1 to 16, and the sums of the numbers in the columns, rows, and two diagonals are equal to each other. Sixth-grader Senya started constructing a magic square and placed the number 1 in some cell. His younger brother Lёnya decided to help him and placed the numbers 2 and 3 in the cells adjacent to the side with the number 1. Will Senya be able to complete the magic square after such help?
The sum of the numbers in each row of the square should be equal to $(1+2+\ldots+15+16): 4=34$. Let's consider two cases:

1) Suppose Lёnya placed the numbers 2 and 3 in the same horizontal or vertical row with the number 1. Then in this row, there is one free cell left, where the number $34-(1+2+3)=28$ must be placed. However, such a number cannot exist in this magic square.
2) Suppose Lёnya placed one of these numbers in the same horizontal row with the number 1, and the other in the same vertical row. Then in the row where 2 is placed, the sum of the numbers in the remaining cells is $34-(1+2)=31$. Therefore, the numbers 15 and 16 must be in this row. But in the row where 3 is placed, the sum of the numbers in the remaining cells is $34-(1+3)=30$. Therefore, the numbers 16 and 14 must be in this row. However, the number 16 cannot be placed in both rows, as the intersection of these rows already has the number 1. Therefore, Senya will not be able to form a magic square.

## Answer

He will not be able to.