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    Number Code Puzzle

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    4. An AE student named Seoung devises a coded system of arithmetic for keeping his financial information private. His coded system of arithmetic is identical to the usual one except that each digit 0 to 9 has a value different than from standard arithmetic.
    The following five equations hold in Seoung's arithmetic:
    (a) 8×7 = 8
    (b) 4×9 = 39
    (c) 7-33 = -1
    (d) 51÷2 = 2
    (e) 7^4 = 6.
    What is the sum 40 + 04 in Seoung's arithmetic expressed in his new digits?

    © BrainMass Inc. brainmass.com October 9, 2019, 10:41 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/number-code-puzzle-228875

    Solution Preview

    I break it as follows.
    8 --> 0
    7 --> 2
    3 --> 1
    1 --> 9
    5 --> 4
    2 --> 7
    4 --> 3
    6 --> 8
    9 --> 5
    0 --> 6

    Thus 40 + 04 = 46 + 64 = 110
    The answer is 110.

    How to decode?
    Step 1: From (a), 8x7 = 8, and (c) 7-33 = -1, we first know that 7 can not be 0. If 7 is 0, 7-33 should be two digits, not -1.
    So 8 has to be 0 or 1. But from (c), 3 has to be 1 ...

    Solution Summary

    This provides an example of working out a number code.

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