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8 November, 02:21

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

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  1. 8 November, 02:46
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    Step-by-step 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
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