How to Solve Nonograms, Sudoku, Kakuro and Futoshiki: Beginner's Guide

Logic grids look like four different hobbies — pictures, digits, sums, inequalities — but they are one skill in four costumes. In every case you are given constraints, and the job is to find the cell whose value is already decided by them, fill it, and look again. Nothing is ever guessed. If you are guessing, you have missed a deduction somewhere.

This guide covers the rules and two or three core techniques for each of the four most common grids, with small worked examples. Once these moves are automatic, almost any daily puzzle at beginner size will fall to them.

Why learn to solve without guessing?

Guessing works on small puzzles and collapses on large ones: a wrong guess fifteen moves back is almost impossible to unwind. Deduction scales. It is also the part that trains anything. Reasoning practice is the second-best-evidenced form of brain training there is: in the ACTIVE trial’s ten-year follow-up, 73.6% of adults who had a short course of reasoning training were at or above their baseline a decade later, versus 61.7% of controls (Rebok et al., 2014). Guessing your way through a grid gives you none of that.

A logic puzzle is a conversation with the constraints. Each filled cell is a question answered; each marked empty cell is a question closed.

How do you solve a nonogram (picross)?

Rules. A grid with clues on each row and column. A clue like “3 1” means the row contains a run of 3 filled cells, then at least one empty cell, then a run of 1, in that order. Fill the grid so every row and column matches its clues. Games: Pixel in Wiseroll, Picross, Griddlers.

Technique 1: overlap

If a run is longer than half the row, its middle must be filled whichever end it sits at. Formally: for a single clue of length k in a row of length n, cells from position n − k + 1 to k are certain.

Worked example: a 10-wide row with the single clue 7.

Position	1	2	3	4	5	6	7	8	9	10
Leftmost placement	X	X	X	X	X	X	X	.	.	.
Rightmost placement	.	.	.	X	X	X	X	X	X	X
Certain				X	X	X	X

Cells 4 to 7 are filled in both extremes, so they are filled. Overlap works with multiple clues too: slide the whole clue set as far left as it goes, then as far right, and fill anything both placements cover.

Technique 2: edge logic

Once a filled cell is anchored against the border or a known empty cell, the clue nearest that edge is pinned. In a row with clue 4 where cell 1 is known filled, cells 1–4 are the run and cell 5 is empty. The same applies from the other direction and from any interior cross you have placed.

Technique 3: count the gaps

Rows whose clues plus the mandatory single gaps exactly fill the row are fully determined. Clue 2 3 2 in a 9-wide row needs 2+1+3+1+2 = 9 cells, so the row reads X X . X X X . X X with no choice. Also mark empties aggressively: a cell that no legal placement can reach is a cross, and crosses create new edges.

How do you solve sudoku?

Rules. Fill the grid so each row, each column and each box contains every digit exactly once. The classic is 9×9 with 3×3 boxes; beginners should start with 4×4 or 6×6 (Mini Sudoku in Wiseroll uses small grids for the daily puzzle).

Technique 1: naked single

A cell whose row, column and box already contain all digits but one. That cell must be the remaining digit.

Worked example, 4×4 grid (boxes are 2×2):

	c1	c2	c3	c4
r1	1	?	3	.
r2	.	4	.	.
r3	.	.	.	.
r4	.	.	.	.

Cell r1c2: row 1 has 1 and 3, its box (r1–r2, c1–c2) has 1 and 4. Candidates 1, 2, 3, 4 minus {1, 3, 4} = 2. A naked single.

Technique 2: hidden single

A digit that has only one legal home within a row, column or box, even if that cell has other candidates. Scan one digit at a time: “where can 7 go in this box?” If the answer is one cell, place it. Hidden singles are usually what unlocks a grid when naked singles dry up.

Technique 3: naked pair

Two cells in the same unit that share exactly the same two candidates — say both can only be 2 or 5. Between them they use up 2 and 5, so remove 2 and 5 from every other cell in that unit. The pair is not placed yet, but the elimination often produces a single elsewhere.

Work in that order: singles first, then pairs, then write candidates only when stuck. A grid that needs more than pairs is above beginner level.

How do you solve kakuro?

Rules. A crossword of numbers. Each horizontal and vertical run has a clue giving its sum. Fill each run with digits 1–9, no repeats within a run, adding to the clue. Game: Sums in Wiseroll.

Technique 1: unique combinations

Some clue-and-length pairs have exactly one solution. These are the kakuro equivalent of givens.

Cells	Sum	Only combination
2	3	1, 2
2	4	1, 3
2	16	7, 9
2	17	8, 9
3	6	1, 2, 3
3	7	1, 2, 4
3	23	6, 8, 9
3	24	7, 8, 9
4	10	1, 2, 3, 4
4	11	1, 2, 3, 5
4	29	5, 7, 8, 9
4	30	6, 7, 8, 9

Pattern: the smallest and largest sums for a given length are unique, and the next ones in are unique too.

Technique 2: cross-reference

Where two runs intersect, the shared cell must belong to both combination sets. Worked example: a horizontal run of 2 cells summing to 4 (so {1, 3}) crosses a vertical run of 3 cells summing to 7 (so {1, 2, 4}). The shared cell must be 1, the only digit in both sets. That places 1, makes the other horizontal cell 3, and leaves {2, 4} for the rest of the vertical run.

	Horizontal 4 (2 cells)	Vertical 7 (3 cells)	Shared cell
Allowed digits	1, 3	1, 2, 4	1

Technique 3: the leftover

If a run of n cells has n − 1 filled, the last cell is the clue minus their sum. Obvious, but it is the move that finishes most grids, so check for it after every placement.

How do you solve futoshiki?

Rules. An N×N grid (usually 4 to 7). Fill each row and column with 1 to N, each once — sudoku without boxes — while obeying the < and > signs between some neighbouring cells. Game: Order in Wiseroll.

Technique 1: inequality chains

Follow the signs from cell to cell. A chain of k cells linked by inequalities needs k distinct, increasing values. In a 4×4, a chain of 4 is forced: 1 < 2 < 3 < 4.

Worked example, 4×4, top row with signs between every cell:

c1		c2		c3		c4
?	<	?	<	?	<	?

The row must be 1, 2, 3, 4. Shorter chains give limits rather than values: in a chain a < b < c, a cannot be 3 or 4 and c cannot be 1 or 2.

Technique 2: minimum and maximum bounds

Every cell has a floor and a ceiling from the inequalities touching it. A cell that must be greater than two different neighbours has a floor of 3. A cell that must be less than a cell whose ceiling is 2 must be 1. Write these bounds lightly and update them whenever a neighbour is placed.

Technique 3: row-column elimination

With bounds in place, switch to sudoku logic. If 4 has only one legal cell in a row after bounds are applied, that is a hidden single. If a cell’s bounds leave one candidate, that is a naked single. Alternate between the two until the grid falls; futoshiki puzzles are designed so that one of the two is always available.

How do the four puzzles share one method?

Puzzle	The “given”	The core move	What to mark as you go
Nonogram	Long clues (overlap)	Pin runs against edges	Crosses in unreachable cells
Sudoku	Crowded rows, columns, boxes	Naked and hidden singles	Candidates only when stuck
Kakuro	Unique sum combinations	Cross-reference intersections	Allowed digit sets per run
Futoshiki	Long inequality chains	Bounds, then singles	Floor and ceiling per cell

In every case the loop is identical: find what is forced, commit it, note what it rules out, scan again. Speed comes from scanning in a fixed order so you do not miss the easy cell. Solving ten small grids a week builds that scan faster than one large grid on Sunday, which is why daily-puzzle sizes exist; the broader case for small daily practice is in microlearning: five minutes a day.

Where to start

Pick one puzzle and one size: a 5×5 nonogram, a 4×4 sudoku, a kakuro with two- and three-cell runs, or a 4×4 futoshiki. Solve it using only the techniques above, saying each deduction to yourself as you make it. When you finish three in a row with no mistakes, go up a size. When you get stuck, do not guess; go back to the table and ask which of the four “givens” you have not checked yet. It is almost always there.