## Task 3 - 220623

The number 32 is to be decomposed into a sum of four natural numbers, which must satisfy the following property.

If you add 3 to the first summand, subtract 3 from the second, multiply the third by 3, and divide the fourth by 3, then the four results you obtain are all equal.

Name four such summands!

Verify that they meet all the requirements! Prove that the requirements cannot be met by any other summands!
Suitable addends are 3, 9, 2, and 18 in this order; because it holds that $3+9+2+18=32$ as well as $3+3=9-3=2 \cdot 3=18: 3=6$.

If the first addend were a smaller (or larger) number than 3, then adding 3 would result in a smaller (or larger) number than 6. Consequently, the second addend would have to be smaller (or larger) than 9, the third smaller (or larger) than 2, and the fourth smaller (or larger) than 18. According to this, the sum would be smaller (or larger) than 32, which contradicts the requirement of the problem.

Therefore, the first addend must be 3, from which it follows that no other numbers than those given above can meet the requirements of the problem for the other addends.