Siamese Method - The Method

The Method

The method was surprising in its effectiveness and simplicity:

"I hope that it will not be unacceptable that I give the rules and the demonstration of this method, which is surprising for its extreme facility to execute a thing, which has appeared difficult to our Mathematicians" —Simon de la Loubère, A new historical relation of the kingdom of Siam.

First, an arithmetic progression has to be chosen (such as the simple progression 1,2,3,4,5,6,7,8,9 for a square with three rows and columns (the Lo Shu square)).

Then, starting from the central box of the first row with the number 1 (or the first number of any arithmetic progression), the fundamental movement for filling the boxes is diagonally up and right (↗), one step at a time. When a move would leave the square, it is wrapped around to the last row or first column, respectively.

If a filled box is encountered, one moves vertically down one box (↓) instead, then continuing as before.