Question

Write down a 3-digit number where digits are in decreasing order. Reverse the digits and subtract it from the first number.

Answer 1

Explanation:

987 → 789

987 - 789 = 198

876 → 678

876 - 678 = 198

765 → 567

765 - 567 = 198

654 → 456

654 - 456 = 198

543 → 345

543 - 345 = 198

432 → 234

432 - 234 = 198

321 → 123

321 - 123 = 198

Generally it is always like that:

3 ≤ x ≤ 9

100x + 10(x-1) + (x - 2) → 100(x - 2) + 10(x - 1) + x

(100x + 10(x - 1) + (x - 2)) - (100(x-2) + 10(x-1) + x)

= 100x + 10(x - 1) + (x - 2) - 100(x - 2) - 10(x - 1) - x cancel 10(x - 1)

= 100x + x - 2 - 100x + 200 - x cancel 100x and x

= 100 - 2

= 198