Question

Try to fill in the missing numbers

Answer 1

9514 1404 393

Answer:

  [[274][895][136]]

Step-by-step explanation:

Starting with the middle row, we need a product of two single-digit numbers that is between 53-1 = 52 and 53-9 = 44. Possible products are 5×9=45 and 6×8=48. This means the number in the middle position in the left column must be 8 or 5.

The middle number in the left column cannot be 5, because we must be able to get -5 by subtracting that number from a sum that is at least 3 = 1+2. So, the middle number in the left column is 8, the other two numbers in that column are 1 and 2, and the other two numbers in the middle row are 5 and 9.

There is no product of single-digit numbers that is 30-1 = 29, so the upper left number must be 2, and the bottom left number must be 1. The other two numbers on the top row must be 4 and 7, so that row's equation is 2+4×7=30.

The only remaining digits are 3 and 6. In order to have -3 on the bottom row, the equation there must be 1×3-6 = -3. Then the middle digit must be divisible by 3, so must be 9.

Our solution is ...

row 1: 2 + 7 × 4 = 30

row 2: 8 + 9 × 5 = 53

row 3: 1 × 3 - 6 = -3

And that makes the column equations be ...

col 1: 2 - 8 + 1 = -5

col 2: 7 + 9 / 3 = 10

col 3: 4 × 5 - 6 = 14