Kakuro

Overview

Kakuro is a numerical crossword built from intersecting sums. Each white square receives a digit from one to nine. A clue before a horizontal or vertical run gives the sum of the digits in that run, and no digit may repeat within the same run. A cell usually participates in both an across sum and a down sum, so its value must satisfy both simultaneously. Black clue cells separate runs; there are no Sudoku boxes or requirement to use every digit in a whole row. Where Sudoku hides its logic in placement alone, Kakuro hides it in arithmetic: the set of digit combinations that can reach a target is often tiny, and the crossing run decides the order. This local pzpr implementation starts with one introductory five-by-five board. A practice selector offers rotations and reflections of that same board, explicitly labelled as orientations rather than separate authored levels or an endless puzzle generator.

How to Play

Select a white answer square and type a digit, or use the on-screen number buttons. On a phone, tap the square before choosing the digit. Use the erase button to remove an entry and Undo to reverse your latest action. Read the diagonal clue cell carefully: the number below the diagonal belongs to the across run on its right, and the number above the diagonal belongs to the down run beneath it. Confusing the two is the most common input error on a new board. Press Check answer when you want feedback about the current arrangement. Restart clears your answers on the selected orientation. Changing the practice orientation also starts a clean attempt on the transformed introductory board.

Tips & Strategy

Start with short runs whose target admits very few distinct-digit combinations. A two-cell sum of three must use one and two, while a two-cell sum of seventeen uses eight and nine. Intersect those candidate sets with the perpendicular run to determine order. Remember that a valid sum with a repeated digit is still invalid. Track combinations for the whole run instead of placing numbers independently until the total happens to match. When checking an error, inspect both sums through the selected cell. Rotated practice boards preserve the same underlying puzzle, so use them to practise reading clue directions rather than expecting new logical content. Resist the urge to fill a long run by trial and error; decompose it against the crossings first, or you will accumulate digits that each look plausible but cannot coexist.

Key Sum Combinations

Every experienced solver memorises the extreme combinations, because they behave like givens:

• Two cells summing to three: only one and two. Two cells summing to four: only one and three, since two and two would repeat a digit.
• Two cells summing to sixteen: only seven and nine. Two cells summing to seventeen: only eight and nine.
• Three cells summing to six: only one, two and three. Three cells summing to seven: only one, two and four.
• Three cells summing to twenty-four: only seven, eight and nine. Three cells summing to twenty-three: only six, eight and nine.

Near-extreme targets are almost as tight. A three-cell run totalling eight, for instance, must contain a one and a two. Writing the candidate set beside a run, rather than a single guessed digit, turns these patterns into immediate eliminations at every crossing.

A Worked Crossing

Here is the classic two-run intersection. A horizontal two-cell run must total three, so its digits are one and two in some order. Its first cell is crossed by a vertical two-cell run totalling four, whose digits must be one and three. The shared cell has to belong to both sets, and the only common digit is one. That single overlap resolves the entire corner: the across partner is two, the down partner is three, and no guessing was involved.

The general habit behind this example matters more than the numbers. Whenever a run narrows to one combination, immediately check every run crossing it for digits that appear in only one shared position. Beginners often do the opposite, committing a digit in one run and only later discovering the perpendicular sum cannot be reached. Checking both sums through a cell before confirming it prevents nearly all of these dead ends.