16×16 Sudoku

About 45% of the cells are given, a much higher share than on a classic board, and there are two levels, Easy and Medium, with 60 stored puzzles each. It is a long, careful solve built on the same techniques as classic Sudoku.

How does a 16-symbol board work?

The board has sixteen rows, sixteen columns and sixteen 4×4 boxes, and you place the symbols 1 to 9 followed by the letters A to G, which stand for 10 to 16. Each row, column and box must hold all sixteen once. The rules page restates this with the other boards. From the keyboard you type the digits 1 to 9 and the letters A to G directly. On the touch pad the sixteen symbols are arranged in two rows of eight. The controls page lists every key.

Each cell sees thirty-nine others: fifteen in its row, fifteen in its column and nine more in its box that are not already in its row or column. A classic cell sees twenty. More peers per cell means each placement removes a candidate from more cells, but each cell also starts with sixteen possibilities to eliminate.

Why does the board have so many givens?

The stored puzzles hold between 110 and 120 givens. The Easy puzzles average 116, and the Medium puzzles all have exactly 110. Against the 256 cells, that is roughly 43% to 47% filled, while a classic puzzle is about 30% filled. The reason is practical. Building a 16×16 puzzle with the technique solver in the loop is slow, so the generator uses a floor for the number of clues it keeps: 120 for Easy and 110 for Medium. The Medium puzzles all sit at that floor. Every puzzle is still verified to have exactly one solution and is graded the normal way, and the stored record includes the solution so your browser never has to search for it.

What do the two levels need?

In the 60 puzzles per level:

• Easy: naked singles in every puzzle, and hidden singles in 98%.
• Medium: pointing pairs in 98%, box/line reduction in 72%, naked pairs in 50% and hidden pairs in 33%.

There is no Hard, Expert or Evil level, because the generator did not produce 16×16 puzzles at those levels. The Medium profile resembles the 6×6 board and the classic board’s Medium in that pointing pairs are almost universal, but here box/line reduction is more common, at 72% against 30% on classic. The box/line reduction lesson is worth reading before you start Medium.

How to tackle a board this size

1. Work one symbol at a time. Pick a symbol that is already placed many times, and walk through the sixteen boxes looking for the one cell where it fits. Hidden singles dominate Easy.
2. Use the pad as a progress tracker. When all sixteen copies of a symbol are on the board, its button is dimmed and struck through, so you can see at a glance which symbols are finished. The count includes any wrong entries, so check that a finished symbol is correct.
3. Be selective with notes. A full set of sixteen candidates in every cell is unreadable on a phone. Mark only the cells you are working on, or use Auto-notes once and then maintain the result. The pencil marks guide explains both.
4. Scan a band at a time. A band of four rows contains four boxes, and a symbol can appear only once in each, which narrows the options quickly.
5. Take breaks. A solve takes much longer than on a 9×9 board. The game pauses automatically when you switch away and saves the board in your browser.

What is it like on a phone?

The grid scales to the width of the screen, so each cell is small. It works best on a larger phone or a tablet, with Large digits switched on in the settings. See Sudoku on mobile for the settings that help, and use digit-first mode to place the same symbol in several cells in a row.

What mistakes are specific to this board?

• Forgetting that A to G are real symbols. Each must appear once in every row, column and box, exactly like the digits 1 to 9.
• Counting a box as 3×3. Here every box is 4×4, with sixteen cells.
• Giving up on notes too early. On a board this size a missed candidate is easy to lose.

The common mistakes guide covers the general errors.

Where does it fit?

It is a different kind of challenge from the harder 9×9 boards: longer, not more intricate. If you would like to build up to it, the 6×6 board introduces rectangular boxes, and the classic board on the home page introduces pointing pairs. The 4×4 board is its smallest relative, and the diagonal board is a shorter way to meet an extra rule. The games hub lists every board.