New: this game comes with the next update of the app.
Cage Sums guide
How to play Cage Sums
Cage Sums is a 9×9 number puzzle with dashed cages. The numbers 1 to 9 go once into every row, column and box, and the digits in each cage add up to its small sum. Hardly any numbers are given: the sums are your clues.
Cage Sums rules
The rules in one minute
Everything from the number puzzle still holds. The cages add one more rule, and the 45 follows from the two.
- Same rules as Sudoku. Every row, column and 3×3 box holds 1 to 9 exactly once.
- Each dashed cage adds up to its small number. The sum sits in the cage’s top-left cell. Here the three digits make 14.
- No digit twice in a cage. 10 from two cells can be 3 and 7, but never 5 and 5.
- Every row, column and box adds up to 45. That is simply 1 + 2 + … + 9. It is the most useful sum of all.
You never have to do more than add small numbers. Every level in Beasties has exactly one solution, and you can always reach it by logic, without guessing.
How to play
Cage Sums in Beasties, step by step
The board in the middle, tools and number pad right below it, and your monster peeking over the top edge.
- Pick a cell. Its row, column and box light up, so you see at a glance which numbers are taken.
- Tap a number. The small count under each key shows how many of that number are still missing.
- Take notes. With Notes on, numbers go in as small candidates. Perfect for the cages of the harder levels.
- Undo and erase. Undo takes back your last step, Erase empties a cell. Both are free.
- Hint, if you must. A hint fills the selected cell, or the easiest one, for 30 stars. After a hint the round gives two stars at most.
Tutorial
Level 0 shows you the cages
The first time you open Cage Sums, a short tutorial starts: a nearly finished grid with four empty cells. Gnatz walks you through the first two.
- A real puzzle, almost done. Only four cells are empty. Gnatz shows you the rows first, then the cages.
- Your first cage. 1 + 4 + ? = 14: the empty cell can only be a 9. Then a cage of two with the sum 3, which is always 1 and 2.
- The rest is yours. Fill the last cells on your own. Wrong numbers cost a star, just like in every level.
You can replay the tutorial any time: it is level 0 at the start of Chill.
Stars and mistakes
Three stars at stake in every level
You start every level with three stars. A wrong number costs one, so it pays to be sure. There is no timer.
- A mistake costs a star. A wrong number turns red right away and one of your three stars falls.
- Three mistakes: try again. With all three stars gone the level is lost. You start the same puzzle again.
- Solve it, keep them. The stars you have left fly into your counter. Spend them on monster parts, hints and level packs.
Notes and Undo are free. A hint costs 30 stars: it fills the selected cell, or the easiest one. After a hint the level gives two stars at most.
Combinations
Sums with only one answer
Some sums can only be made one way. Spot them and you know which digits go into a cage before you know where. These twelve are worth learning by heart.
- Two cells. 3, 4, 16 and 17 have one answer each.
- Three cells. 6, 7, 23 and 24: the smallest and the largest sums.
- Four cells. 10, 11, 29 and 30. Bigger cages follow the same idea.
The trick works for bigger cages too: a sum close to the smallest or the largest possible total leaves very few choices. A cage of two cells can never hold the same digit twice, so 4 is always 1 and 3, never 2 and 2.
Difficulty levels
Four difficulties, 999 levels each
The boards below are level 1 of each difficulty. Each step down gives you fewer numbers and bigger cages, and asks for a harder idea, from plain cage sums in Chill to sums across several rows in Devilish. None of them ever needs a guess.
Chill
18 given · cages up to 4
Small cages and many numbers given. Perfect to warm up.
Normal
0–6 given · cages up to 5
Hardly any numbers given. Cage sums show the way.
Tricky
none given · cages up to 6
Not a single number given. Every row, column and box adds up to 45.
Devilish
none given · cages up to 7
Big cages, nothing given. Add up across several rows. Never guesswork.
Chill, Normal and Tricky have 150 free levels each. You unlock the rest for free with the stars you win, or all at once with Pro. Every player gets the same puzzles in the same order, so the solutions on this site match your app, from level 1 to 999 on every difficulty.
Cage Sums techniques
From the first cage to the last
Beasties rates every level by the hardest idea it needs. Here they are from easy to hard, each with the difficulty that first asks for it. Every example comes from a real level of the app.
Technique 1 · Chill
One way to make the sum
A cage whose sum has only one set of digits tells you what goes in. A number nearby in the same row, column or box then tells you which digit goes where. Enough for Chill.
- Only one way to make it. Two cells, sum 16: that is always 7 and 9. Write both as notes.
- Look around the cage. One cell already has a 9 in its column, so it can’t be that number.
- Both cells are solved. It gets the 7, and the other cell takes the 9.
Technique 2 · Normal
It must be in this cage
Write down every way the cage can make its sum. If one digit shows up in all of them, the cage holds it. When that digit can only sit in one row, column or box inside the cage, it leaves the rest of that line. The key to Normal.
- List the ways. With the notes around it, this cage can make 9 in 2 ways.
- The 2 is in every one. So the cage holds a 2 for sure. Inside the cage it can only sit in one column.
- Cross it out elsewhere. That column gets its 2 from the cage, so no other cell of it can have one.
Technique 3 · Tricky
The 45 rule
The digits of every row, column and box add up to 45. Add the cages that lie completely inside one of them: what is missing to 45 belongs to the cells that are left. If only one cell is left, you have its number. This is where Tricky starts.
- One box: 45. Its nine digits add up to 45, whatever they are.
- Take away the whole cages. 2 cages lie completely inside. Subtract their sums.
- One cell is left over. What is missing to 45 is its number: 2.
Technique 4 · Devilish
45 across several rows
Two rows add up to 90, three to 135. Taking several rows or columns together catches cages that a single line cuts in half. Devilish also asks for pairs, X-Wing and XY-Wing from the number puzzle.
- Take two columns: 90. Each one adds up to 45, so together they make 90.
- Take away the whole cages. 6 cages lie completely inside. Subtract their sums.
- One cell is left over. What is missing to 90 is its number: 9.
Tip: start with the smallest and the largest sums, they have the fewest combinations. Then look for rows, columns and boxes that are almost covered by whole cages. The classic techniques still work too: the Sudoku guide shows pairs, X-Wing and XY-Wing step by step.
Solutions
Stuck on a level?
Every level has its own solution page, free and Pro. You see the puzzle with its cages first, reveal one number at a time, and open the whole grid only if you want to.
FAQ
Cage Sums questions, short answers
What are the rules of Cage Sums?
Fill the 9×9 grid so that every row, column and 3×3 box holds the numbers 1 to 9 once. On top of that, the digits in each dashed cage add up to the small number in its corner, and no digit appears twice in a cage.
How is it different from Sudoku?
The grid and the rules are the same. The difference is the clues: instead of many given numbers you get cages with sums. From Tricky on, not a single number is given.
Can a digit repeat inside a cage?
No. A cage never holds the same digit twice, even when it spans two boxes. That is why a cage of two cells with the sum 4 is always 1 and 3.
What is the 45 rule?
The numbers 1 to 9 add up to 45, so every row, column and box does too. Subtract the cages that lie completely inside a row, column or box from 45, and you get the sum of the cells that are left.
Where do I start?
With the cages that have only one way to make their sum, like 3 or 17 in two cells. Then use the given numbers and the rows, columns and boxes around them.
Do I ever have to guess?
No. Every level has exactly one solution and logic always gets you there. Devilish asks for the 45 rule across several rows and some classic patterns, but never for trial and error.
Can I look up the rules during a round?
Yes. Tap the gear at the top left of the round: Settings open, and their Game guide row takes you straight to the rules of this game, what is special in it and how the stars work. You also find the guide behind the ? on the level start and in Settings on the home screen.
What happens after three mistakes?
Every wrong number costs one of your three stars. With all three gone the level is lost and you start the same puzzle again. Stars from earlier levels stay yours.
What does a hint cost?
A hint costs 30 stars and fills the selected cell, or the easiest one if none is selected. A level with a hint gives two stars at most. Notes and Undo are free.
Is there a timer?
No. Cage Sums has no clock. Take as long as you like, offline and without ads.