Puzzle 116: The Largest Total

Solution

The lines that have to match are the four that run through the middle square (the European wording says this outright): the middle row, the middle column and the two diagonals.

1. The middle number is counted in all four lines, so to make the shared total as large as possible, put the biggest number allowed — **51** — in the middle. 2. The other eight squares form four opposite pairs, one pair for each line. Each pair needs the same sum. Using the next-largest numbers, 43 to 50, works: 50 + 43 = 49 + 44 = 48 + 45 = 47 + 46 = 93. 3. Each line then totals 93 + 51 = 144.

The middle square holds **51**.

*Note:* if you read the North American wording as a full magic square, where every row and column must match, the middle number of any 3 × 3 magic square has to be exactly one third of the line total, so 51 would be impossible. The game's intended reading is the four lines through the middle.