Directive 13: Magic Square (Hints & Answer)

Hint first (no full spoiler): Every row, column, and diagonal of the square adds to the same number. Find that number from a complete line, then work out what the empty cell must be.

Directive 13 presents a 3x3 magic square on the rule card with one cell blanked out. In a magic square, every row, every column, and both diagonals add up to the same number. The Vault Security Committee has hidden one cell and would like it back. Your password must contain the missing number.

The full solution

You never need algebra, just two subtractions:

1. Find the magic sum. Look for any complete line: a row, column, or diagonal with all three numbers visible. Add them. That total is the magic sum for the whole square.
2. Find the broken line. Take any row or column that passes through the empty cell.
3. Subtract. Magic sum minus the two visible cells in that line equals the missing number.

Worked example. Suppose the card shows:

2	7	6
9	5	1
4	?	8

The top row is complete: 2 + 7 + 6 = 15, so the magic sum is 15. The bottom row shows 4 and 8, so the missing cell is 15 - 4 - 8 = 3. Type 3 into your password.

Values stay small, single digits up to the low teens, so the arithmetic is quick. Example fragments that pass (with answer 3): chad1221!3, 3nepal-otto, Fern44x3.

Sanity check before you commit: verify your answer against a second line through the empty cell (the column, or a diagonal if it applies). If both lines agree, the Committee will too.

What breaks later

Another required number means another entry in your digit ledger:

• Directive 8 counts the new digits immediately. A missing number of 3 adds 3 to your digit sum; a missing number of 12 adds 1 + 2 = 3 as well, which is a small mercy. If the sum falls off a perfect square, adjust elsewhere.
• Your Directive 9 answer is already in the password. Keep the two numbers visually separated (a symbol between them) so you can audit each one when a rule floats up DENIED. But remember symbols also break palindrome runs for Directive 11, so do not slice through your 1221.
• If the missing number is a repeated digit like 11, note that it slots neatly into a digit palindrome. The Committee does not reward efficiency, but it does not forbid it.

The square is randomized per run. Copying a friend’s answer is both cheating and, per Committee records, statistically fatal. Fern saw nothing.

Stuck on a different directive? Browse all 30 rule guides or return to the vault. Fern believes in you.