Benjamin Franklin's Magic Square
| 52 |
61 |
4 |
13 |
20 |
29 |
36 |
45 |
| 14 |
3 |
62 |
51 |
46 |
35 |
30 |
19 |
| 53 |
60 |
5 |
12 |
21 |
28 |
37 |
44 |
| 11 |
6 |
59 |
54 |
43 |
38 |
27 |
22 |
| 55 |
58 |
7 |
10 |
23 |
26 |
39 |
42 |
| 9 |
8 |
57 |
56 |
41 |
40 |
25 |
24 |
| 50 |
63 |
2 |
15 |
18 |
31 |
34 |
47 |
| 16 |
1 |
64 |
49 |
48 |
33 |
32 |
17 |
- Every strait row (horizontal or vertical) of 8 numbers added together makes 260, and each half row half 260.
- The bent row of 8 numbers, ascending and descending diagonally, viz, from 16 ascending to 10, and from 23 descending to 17, makes 260; likewise all parallel bent rows.
Also the bent row from 52 descending to 54 and from 43 ascending to 45 make 260; and all parallel rows.
Also the similar bent rows vertically, in both directions, and their parallels.
- The shortened diagonals from 53 to 4 ascending, and from 29 to 44 descending, together with the two corners, make 260; And likewise at the opposite side, and vertically on both sides.
Also the two numbers 14, 61 ascending and 36, 19 descending, with the lower four numbers situated like them, viz. 51, 1 descending and 32, 47 ascending, make 260.
- The four corner numbers with the 4 middle numbers, make 260.
"So this magical square seems perfect in its kind. But these are not all its properties; there are 5 other curious ones, which, at some other time, I will explain to you." -- B. Franklin
Place the numbers 1 through 9 in the square below to make a magic square, in which each row, column, and the two diagonals add up to the same number.
Hints: What number should go in the center space?
What is the common sum which the columns, rows, and diagonals add up to?
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