Question

If you were to produce a 3 digit multiple of 7 that has a final digital sum of 7 using the formula; 7(1+9k). How do you calculate what k is?

Answer 1

If I understand the question correctly, we get several constraints from the conditions:

`100 < 7(1+9k) <= 999` to get a 3 digit number with final digit sum = 7.

Dividing all parts by 7 we get

`100/7 < 1+9k <= 999/7`

Subtracting 1 from all parts we get

`93/7 < 9k <= 992/7`

Dividing all parts by 9 we get

`93/63 < k <= 992/63`

So `2 <= k <= 15`

All of these values of `k` give solutions.