When this number is multiplied by the consecutive numbers from 1 to 12 in a particular order it produces a remarkable or ‘mystical’ outcome !

Firstly let’s multiply the number 76923 in by the numbers in the following order: 1, 10, 9, 12, 3 & 4

What do you notice about the set of answers?

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Solution

The answers are cyclic, moreover if you look more closely, you will see that if we follow the answers along their diagonals, they are the same.

mystic-number-76923-2

We can represent these answers in the 6 x 6 square drawn below.

mystic-number-76923-3

Can you identify what type of square this is?

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Solution

These answers can be represented in a Latin Square, (no number is repeated along any row or down any column). Note all right diagonal share the same value. The main right diagonal are all 3’s. The first row and first column is the number 076923.

Secondly, let’s now multiply the number 76923 in by the remaining numbers in the following order: 2, 7, 5, 11, 6 & 8.

What do you notice about the set of answers ?

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Solution

The answers are cyclic and like before the answers along their diagonals are the same.

mystic-number-76923-5

These answers can be represented in a Latin Square, (no number is repeated along any row or down any column). Note all right diagonal share the same value. The main right diagonal are all 6’s. The first row and first column is the number 153846.

mystic-number-76923-6

Now- one, final twist!

Combine the two Latin Squares by adding the values in the same positions in each square.

The resulting “combined” square has a special quality. Can you identify what it is?

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Solution

If we add these two Latin Squares together, we get a Magic Square with a magic sum of 54.