# 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.