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reza
Lv 4
reza asked in Science & MathematicsMathematics · 1 decade ago

Find this 4 digits number.?

abcd is a 4 digits number which abcd=(d-a)^4-(d-a)^3-(d-a)^2

1 Answer

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  • 1 decade ago
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    2009

    (9-2)^4 = 2401

    (9-2)^3 = 343

    (9-2)^2 = 49

    2401-343-49 = 2009

    a must be from 1-9 (if a=0 it would be a 3 digit number) and b,c,d must be from 0-9

    if d-a = 5 or less then we would not end up with a 4 digit number

    so d-a must be 6 or greater

    the highest number d can be is 9 and the lowest number a can be is 1 so d-a can be no higher than 8

    therefore d-a must be 6, 7, or 8

    Fill in each of these numbers for d-a and you'll see that only 7 creates a solution.

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