Ramanujan Magic Square!

The square uses Ramanujan’s birthday (December 22, 1887) to fill the
cells in the top row (by now, you should know how to construct fourthorder magic squares with any given top row).
The author now asks: “What’s so great in this?” and proceeds to answer
the question himself or herself (as is usual with many such mails, one
does not quite know whether the author is a man or a woman—or
indeed who the author is at all!).

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The first point that the author makes is that the row sums are all equal
to 139, and so are all the column sums and the sums of the two main diagonals. (Please check for yourself that this
is so.) This, of course, merely affirms that the
structure is a magic square.

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sum of the numbers in the four central cells is
139.
The sums of the numbers in these like-coloured
2 × 2 blocks are all 139.
And so also in these two coloured 2 × 2 blocks.
We invite the reader to relate all these
observations with the theorems we have proved
about fourth-order magic squares, and then
to appreciate for himself or herself that every
fourth-order magic square has these very same
properties. And that is truly magical indeed.
diagonals. (Please check for yourself that this
is so.) This, of course, merely affirms that the
structure is a magic square.
But now follow several other points of interest:
The sum of the four corner elements of the square

is the same number (note the numbers in the cells
coloured red), i.e., 22 + 87 + 11 + 19 = 139.
The sums of the numbers in the two sets of likecoloured cells are again the same number (139).
The sums of the numbers in the two sets of likecoloured cells here are yet again the same number
(139).
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
The sum of the four corner elements of
the square is the same number (note
the numbers in the cells coloured red),
i.e., 22+87+11+19 = 139.

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sums of the numbers in the two
sets of like-coloured cells are again the
same number (139).

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sums of the numbers in the two
sets of like-coloured cells here are yet
again the same number (139).

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sum of the numbers in the four
central cells is 139.

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sum of the four corner elements of
the square is the same number (note
the numbers in the cells coloured red),
i.e., 22+87+11+19 = 139.

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sums of the numbers in the two
sets of like-coloured cells are again the
same number (139).

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sums of the numbers in the two
sets of like-coloured cells here are yet
again the same number (139).

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sum of the numbers in the four
central cells is 139.

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sum of the four corner elements of
the square is the same number (note
the numbers in the cells coloured red),
i.e., 22+87+11+19 = 139.

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sums of the numbers in the two
sets of like-coloured cells are again the
same number (139).

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sums of the numbers in the two
sets of like-coloured cells here are yet
again the same number (139).

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sum of the numbers in the four
central cells is 139.

22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

The sum of the ncentral cells is 13RAMANUJAN’S MAGIC SQUARE
22 12 18 87

88 17 9 25
10 24 89 16
19 86 23 11

The sums of the like-coloured
2×22 12 18 87

88 17 9 25
10 24 89 16
19 86 23 11
Hope it Helps!

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Credits:
Background Music: Maestro Tlaekelel
Artist: Jesse Gallagher

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