Question

Use the digits 0-9 only once each, so that each expression has the same value

Answer 1

As you can read below, we can write expressions for addition and subtraction, but not for multiplication and division.

Explanation:

We can find out examples for addition and subtraction, this way:

1. Addition:

1 + 8 = 9 1 + 7 = 8 1 + 6 = 7 1 + 5 = 6 1 + 4 = 5

2 + 7 = 9 2 + 6 = 8 2 + 5 = 7 2 + 4 = 6 2 + 3 = 5

3 + 6 = 9 3 + 5 = 8 3 + 4 = 7

4 + 5 = 9

2. Subtraction:

9 - 1 = 8 9 - 2 = 7 9 - 3 = 6 9 - 4 = 5

8 - 1 = 7 8 - 2 = 6 8 - 3 = 5

7 - 1 = 6 7 - 2 = 5

6 - 1 = 5

For multiplication and division we inevitably will repeat any of the digits, like these examples:

8 * 1 = 8 (8 is repeated and therefore not a valid example)

4 * 2 = 8

9 ÷ 3 = 3 (3 is repeated and therefore not a valid example)

3 ÷ 1 = 3 (3 is repeated and therefore not a valid example)

Answer 2

You didn't state the pattern in which you like the expressions to be written. I wrote it nevertheless, and hope that this can help find an answer to your problem if this isn't exactly what you are trying to find.

Explanation:

1. The expressions that result to

9 - 8 = 1

7 - 6 = 1

5 - 4 = 1

3 - 2 = 1

2. The results that result to 9.

8 + 1 = 9

7 + 2 = 9

6 + 3 = 9

5 + 4 = 9