Math board

Complete the blank boxes with the figures from 1 to 9, without repeating any, so that the indicated equalities are met.

Solution

We start with the box at the bottom right. As it must be the sum of two different numbers, it will be greater than or equal to 3 and as it must be a product of two different numbers from each other and different from those added together, it cannot be 3 (it is only 3 * 1), nor 4 ( 2 * 2, 4 * 1), neither 5, nor 7, nor 9. It can only be 6 or 8.

If it were 6, the two numbers that appear on the right, which multiply to get 6, will be 2 and 3, but I don't know in what order. One of them is the result of dividing two and the other of subtracting two others. The 3 cannot be the result of dividing two different numbers, because we would need the 6 and it is already used. That means that it must be 2 and it can only be 8 divided by 4. But then, 3 is the difference of two and that we cannot achieve because all the necessary numbers are used.

Therefore it is 8. We get it by multiplying 2 by 4. The number 4 can only be achieved with a division that uses 8 and is therefore impossible. Then the 2 will be the result of a division, 6 by 3. The sum that gives 8 must be achieved with 1 and 7 (and these numbers are interchangeable), since 2, 3 and 4 are already used. And finally, 4 is simple to obtain with the two remaining numbers, 9 minus 5. The square is as we see below.