woensdag 1 januari 2020

A very special Magic Square

A magic square with in de centre the lowest numbers 1 -256.
The numbers are organised so that 1-4 are in the centre. 
Around there is a layer from the numbers 5 -16.
In the next layer around the numbers 17-36
And so on:
37-64
65-100
etc and the last (outside) layer 193-256

The square is magic because the sum of the numbers in each row, column and all diagonals are the same: 131104

The extra in this square is that in this centre the 2 by 2 squares are connected
The sum of the middle 2x2 square: 10
1+2+3+4
The sum 2x2 squares of the layer around is 34
16+7+10+1 and 8+15+2+9 and 12+3+14+5 and 4+11+6+13
The sum of de 2x2 squares in the layer around is 82
25+18+23+16 and33+34+7+8 and 17+26+15+24 and 9+30+11+32 etc
in the next layers the sum of the 2x2 squares are:
162 - 274 - 418 - 594 and 802

The centre with the layers
and the total 64x64 square



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