Table of mathematical expressions - fill in 1-9

The number $9$

Option 1:

Option 2:

So the full solution is

Here's another way to solve this puzzle. We can actually proceed one digit at a time, and the middle column product trick (see below) seems way too neat to be a coincidence.

Step 1: Where can the 1 go?

• It can't be in the rightmost column (it's too small to be subtracted, and if it's added, the other two digits in the column would have to be equal to each other)
• It can't a part of either product (can't reach the high totals), and
• It can't be in the top row's addition (can't reach 12 in the row).

So the

Step 2: The three rows contain only additions and a single subtraction. The row totals add up to 35, and the numbers 1-9 add up to 45, so the subtracted number

Step 3: The product in the middle column is now very limited. We know it must be a number between 28 and 36. But

• 29 and 31 are prime
• 30 and 35 would need a 5 in the product
• 32 would need a 5 in the addition
• 33 would need an 11 in the product
• 34 would need a 17 in the product, and finally
• 36 would need a 1 in the addition.

Therefore, the product must be 28, which places the

The left column is now easily solved (there are equations with only one number missing) so we know that the remaining two digits at the rightmost column are 2 and 6, and that column's equation fixes the order of the rest of the digits: