## Task 2 - 250622

Four numbers are sought with the following properties:

(1) The sum of the four numbers is 60.

(2) The same result is obtained four times when

(2.1.) 4 is added to the first number,

(2.2.) 3 is added to the second number,

(2.3.) 2 is subtracted from the third number,

(2.4.) 1 is subtracted from the fourth number.

Determine four such numbers from these requirements! Verify that the numbers you have found have the required properties!
I. If four numbers have the required properties and $e$ is the result mentioned in (2), then $e-4$ is the first number, $e-3$ is the second number, $e+2$ is the third number, and $e+1$ is the fourth number.

According to (1), therefore, $e-4+e-3+e+2+e+1=60$ and thus $e=64$; hence, the four sought numbers are: $12,13,18,17$.

II. For the numbers, $12+13+18+17=60$, so (1) is satisfied, and it holds that $12+4=16,13+3=16$, $18-2=16,17-1=16$, so (2) is satisfied.