The letters A, B, C, and D represent four distinct integers from 0 through 9. When A is added to B the result is C. When B is subtracted from A the result is D. How many possible ways are there to assign values to A, B, C, and D?

Hamburger Aug 26, 2024

#1**+1 **

\(a + b = c\)

\(b - a = d\)

\(a < b\)

\(a \neq 0\)

(If a was 0, then b and d would be the same)

If a was 1, b could be any number from 3 - 8 (6 numbers)

If a was 2, b could be 3, 5, 6, 7 (4 numbers)

If a was 3, b could be 4, 5 (2 numbers)

If a was 4, b could only be 5 (1 number)

There are no other possible values for a

Therefore there are 6 + 4 + 2 + 1 = **13 possibilities**.

Maxematics Aug 26, 2024