Volume XII (1200-1299)

1266 - Magic Square

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Difficulty : easy

Solution Description :

Magic Square Problem

The Siamese method, or De la Loubère method, is a simple method to construct any size of n-odd magic squares.

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

Order-3 magic squares

step 1
	1
	.
	.

step 2
	1
	.
		2

step 3
	1
3
		2

step 4
	1
3
4		2

step 5
	1	6
3	5
4		2

step 6
	1	6
3	5	7
4		2

step 7
8	1	6
3	5	7
4		2

step 8
8	1	6
3	5	7
4	9	2

Order-5 magic squares

Step 1
		1
		.
		.
		.
		.


1
.
.
.		3
.	2

Step 3
		1
	5
4		.
				3
			2

Step 4
		1	8
	5	7
4	6	.
				3
			2

Step 5
		1	8	15
	5	7	14
4	6	13
10	12			3
11			2	9

Step 6
17	24	1	8	15
23	5	7	14	16
4	6	13	20	22
10	12	19	21	3
11	18	25	2	9

-adopt from Wikipedia

UVa Problem Hints

1266 - Magic Square

Order-3 magic squares

Order-5 magic squares