Fill each row and column without repeats, read every line in both directions, sort the resulting numerals, and use perimeter ranks as clues. A single edge clue can describe an entire directional number.
Your puzzle is a blank 4×4 grid. Put 1, 2, 3, and 4 once in every row and every column. Read each row and column from both ends. The resulting 16 four-digit numbers must all be different, and their order from smallest to largest must match the ranks outside the grid.
First, learn what a rank means. Reading the row 1 · 3 · 2 · 4 from the left makes 1324; from the right it makes 4231. The digits form one number, rather than being added.
In a separate three-number practice list, 1324 < 2143 < 3412. Their ranks are 1st, 2nd, and 3rd. In the real puzzle, a rank is the position in the list of all 16 directional numbers. An outside “9” means “this whole line-number is ninth smallest”; you do not write 9 in a cell.
1. Read the arrow direction. 2. Build the full numeral. 3. Compare digits from left to right. 4. translate rank bands into edge digits. 5. use the Latin rule to finish the interior.
In an n × n Latin square, each row and each column contains every permitted symbol exactly once. Diagonals do not have to contain every symbol unless the puzzle says so.
Choose a line and direction. The highlighted first cell becomes the highest place value.
Not every Latin square has distinct directional numerals. This original square has all 24 different. That makes the ranks 1 through 24 unambiguous.
Click any perimeter rank. The board highlights the line read by that arrow, then the inspector locates its numeral in the common sorted list.
Compare digits from the left. The first unequal digit decides the order.
| Rank | Numeral | Read from |
|---|
The sixteen rank clues make sixteen first-digit predictions. The four corner cells are predicted twice, so twelve distinct boundary cells are fixed.
For these symbols 1–4 (or 1–6) and distinct directional numerals, a rank tells the first digit immediately. Later digits are used only to order numerals inside the same band.
No hint used yet. Try translating each rank into its first digit.
The worked example prints one completed square. This added audit checks every 4 × 4 Latin square using the symbols 1 through 4 and asks how many satisfy all sixteen perimeter ranks.
Run the audit to reveal the unique matching construction.
| Rank | Numeral | Read from |
|---|