Tally
Put digits 1 to 9 in the empty squares so each run adds up to the number at the start of it. No digit repeats within a run.
- Four levels: Easy to Extra Hard
- 7 techniques on its ladder
How Tally Works
The board is a small grid of grey clue squares and white squares. A number in a grey square is a total, and it heads a run of white squares, reading across or down. The digits you put in that run have to add up to it. Every white square sits in one across run and one down run, so each digit has two totals to satisfy.
Runs are never more than five squares long, so the arithmetic stays small enough to do in your head. Some squares start filled in, and every board has exactly one answer.
Pencil notes let you keep the digits a square could still hold, and Fill Notes pencils in every digit not already used in a square's runs. It leaves the sums to you. A hint names the technique and shows the arithmetic on the card, such as “7 + X = 10, so X = 3”.
The Rules
- 1
Reach the Target
Fill the empty squares with digits 1 to 9 so each numbered run adds up to its total. The number to the right of a grey square heads the across run; the number below it heads the down run.
- 2
No Repeats in a Run
A digit cannot appear twice in the same run, though it may repeat in a different one.
- 3
Given Digits Are Fixed
Digits already on the board when you start stay put. Build your answer around them.
- 4
A Wrong Digit Costs a Heart
A digit that does not belong in a square costs a heart the moment you place it. Changing it to another wrong digit costs nothing more, and notes are always free. In practice you have three hearts a board; in the daily set they never run out.
The real screens.
Every picture on this page is the app itself, on a board from the game.
Where Cross Sums Come From
The puzzle began in the United States as Cross Sums, a name given in 1966 by Jacob E. Funk, a Canadian who worked for Dell Magazines. It reads like a crossword whose clues are totals and whose answers are digits.
The Japanese publisher Nikoli brought it to Japan in 1980 as *kasan kurosu*, “addition cross”, later shortened to kakuro, the name most solvers know it by today.
How the Levels Differ
The grid grows one size a difficulty, and is taller than it is wide so it fills a phone screen. Easy is a 4×6 grid with about 7 squares to work out, each of which can be settled on its own from a run with one gap left. Medium is 5×7 with about 11 squares, and at least once, and at most three times, a board asks you to work out two empty squares of one run together. It never asks for three at once.
Hard is 6×8 with about 20 squares, and at least three times a board you weigh three or four empty squares of a run together. Extra Hard is 7×9 with about 29 squares, does that more often, and at least once hands you a five-square run with every square still empty.
7 techniques, easiest first.
In Dayzle the hint and the solver are one engine, so these are the steps it takes to solve a Tally board, from the first you'll meet to the rarest. Open one for a worked example and a clip of the hint teaching it on a real board.
Run Total Basic A run with one empty square left: its total minus the digits already in it is that square's digit.
Say an across run totals 10 and already holds a 7, with one square empty. 7 + X = 10, so the empty square is 3.
This is the move most boards open with, and on Easy it is nearly the whole game: filling one run's last square often leaves a crossing run with one square left.
Naked Single Beginner A square where only one digit is not already used in its two runs, or with one note left.
Go through 1 to 9 for a square and skip every digit already in its across run or its down run. If only one is left, it goes in that square. With notes, it is a square that has only one note left.
Run Minimums Intermediate The other empty squares of a run take at least 1 + 2 + …, which caps how big each square can be.
Say the four empty squares of a run have to add up to 10. Any three of them take at least 1 + 2 + 3 = 6, with no digit twice. That leaves at most 4 for the fourth, so no square in the run can be more than 4: take out every note above it.
Run Maximums Intermediate The other empty squares of a run take at most 9 + 8 + …, which sets how small each square can be.
Say a run of three totals 16 and already holds a 2, so its two empty squares make 14. The other square can take at most 9, so no empty square in the run can be less than 5: take out every note below it.
Partner Check Intermediate In a run with two empty squares, each note needs a partner that is still pencilled in the other square.
With two empty squares left, whatever goes in one decides the other. Say they must make 8. A 4 in one would need a 4 in the other, which repeats, so 4 comes out of both.
It also works from the notes: if one square is down to 1 or 2, the other can only be 7 or 6, and every other note in it comes out.
Naked Pair Intermediate Two squares in one run with the same two notes and nothing else.
Say two squares in a down run both have only the notes 1 and 3. Between them they use up the 1 and the 3, so every other square in that run loses its 1 and 3 notes.
Sum Combinations Advanced List every way a run's empty squares could still make its total, and drop any note that fits none of them.
Take a run and write out every set of digits its empty squares could still hold, using only what is pencilled in them and no digit twice. Say a run of four totals 11: the only set of four different digits that adds to 11 is 1, 2, 3, 5, so any note outside those comes out.
This is the last thing to try, when run totals, minimums, maximums, partners and pairs have found nothing. Hard and Extra Hard boards need it on runs of three, four and five squares.
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