Thursday, 12 February 2015

The Blue Elephant...

Here's another interesting challenge... this time, from Mr Dean Ang :)

Are you able to 'crack' the mystery behind this?



1 comment:

  1. 1 x 3 = 3, 3 x 3 = 9, 9 + 0 = 9, 9 - 5 = 4
    2 x 3 = 6, 6 x 6 = 36, 3 + 6 = 9, 9 - 5 = 4
    3 x 3 = 9, 9 x 9 = 81, 8 + 1 = 9, 9 - 5 = 4
    4 x 3 = 12, 12 x 12 = 144, 1 + 4 + 4 = 9, 9 - 5 = 4
    5 x 3 = 15, 15 x 15 = 225, 2 + 2 + 5 = 9, 9 - 5 = 4
    6 x 3 = 18, 18 x 18 = 324, 3 + 2 + 4 = 9, 9 - 5 = 4
    7 x 3 = 21, 21 x 21 = 441, 4 + 4 + 1 = 9, 9 - 5 = 4
    8 x 3 = 24, 24 x 24 = 576, 5 + 7 + 6 = 18, 1 + 8 = 9, 9 - 5 = 4
    9 x 3 = 27, 27 x 27 = 729, 7 + 2 + 9 = 18, 1 + 8 = 9, 9 - 5 = 4
    10 x 3 = 30, 30 x 30 = 900, 9 + 0 + 0 = 9, 9 - 5 = 4
    11 x 3 = 33, 33 x 33 = 1089, 1 + 0 + 8 + 9 = 18, 1 + 8 = 9, 9 - 5 = 4
    12 x 3 = 36, 36 x 36 = 1296, 1 + 2 + 9 + 6 = 18, 1 + 8 = 9, 9 - 5 = 4
    13 x 3 = 39, 39 x 39 = 1521, 1 + 5 + 2 + 1 = 9, 9 - 5 = 4
    14 x 3 = 42, 42 x 42 = 1764, 1 + 7 + 6 + 4 = 18, 1 + 8 = 9, 9 - 5 = 4
    15 x 3 = 45, 45 x 45 = 2025, 2 + 0 + 2 + 5 = 9, 9 - 5 = 4
    16 x 3 = 48, 48 x 48 = 2304, 2 + 3 + 0 + 4 = 9, 9 - 5 = 4
    17 x 3 = 51, 51 x 51 = 2601, 2 + 6 + 0 + 1 = 9, 9 - 5 = 4
    18 x 3 = 54, 54 x 54 = 2916, 2 + 9 + 1 + 6 = 18, 1 + 8 = 9, 9 - 5 = 4
    19 x 3 = 57, 57 x 57 = 3249, 3 + 2 + 4 + 9 = 18, 1 + 8 = 9, 9 - 5 = 4
    20 x 3 = 60, 60 x 60 = 3600, 3 + 6 + 0 + 0 = 9, 9 - 5 = 4
    21 x 3 = 63, 63 x 63 = 3969, 3 + 9 + 6 + 9 = 27, 2 + 7 = 9, 9 - 5 = 4
    22 x 3 = 66, 66 x 66 = 4356, 4 + 3 + 5 + 6 = 18, 1 + 8 = 9, 9 - 5 = 4
    23 x 3 = 69, 69 x 69 = 4761, 4 + 7 + 6 + 1 = 18, 1 + 8 = 9, 9 - 5 = 4
    24 x 3 = 72, 72 x 72 = 5184, 5 + 1 + 8 + 4 = 18, 1 + 8 = 9, 9 - 5 = 4

    Key:
    n = integer from 1 to 100
    y = Number after multiplied by 3
    q = Squared number


    n x 3 = 3n, 3 x n x 3 x n = q,
    Digits of q = 9, 9 - 5 = 4
    As you can see, you multiply the number by 3 and square it after that to get 3 x 3 = 9, and it is the reason that 9 is always the sum of the digits of q, because 9 is a multiple of 9. This applies to all the numbers from 1 to 100, so the answer in the end will always be Denmark and an Elephant, because the result is always 9 - 5 = 4.

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