Solvarium

Puzzle guide

How to solve Kurotto

Kurotto is a shading puzzle with circles. Each number counts the filled cells around its circle, but not one by one: it adds up the whole groups that touch it. That one idea is what makes Kurotto different, and this guide shows you how to use it.

The rules

  1. Fill cells. A circle itself always stays empty.
  2. A circle's number is the total size of the filled groups touching it. Each group is counted once, however many of the circle's sides it touches.
  3. A circle without a number counts nothing: anything may touch it.
  4. The filled cells do not have to be connected. Get every number right and the puzzle is done.

A solved puzzle

3202
A solved puzzle. The 3 touches one group of three filled cells. Each 2 touches a group of two, and the 0 touches nothing.

Your first moves

  1. Put an X next to every 0: no filled cell may touch it.
  2. Remember that a group is counted whole: one filled cell next to a circle brings every cell joined to it into the count.
  3. Look for circles with little room around them. If all the room left is exactly enough, fill it.
  4. Before you fill a cell, check it does not join two groups into one that is too big.

Techniques, step by step

A 0 touches nothing

A circle with 0 may not touch any filled group. Put an X on every cell next to it. The same is true for any circle whose number is already met: every free cell that could still add to it gets an X.

0
The 0's four neighbours are empty.

Only one cell left

The 1 in the corner needs one filled cell, and its other neighbour already has an X. So the cell to its right must be filled. Whenever all the room a circle still has is exactly what it needs, fill all of it.

1
Only one cell can fill up the 1.

Too much for the number

The 1 already touches a filled cell, so its count is done. Filling the cell to the right of that filled cell would make the group two cells big, and the 1 would count 2. Filling the cell below the circle would add a second group. Both are too much, so both get an X. Checking whether a cell would push a circle past its number is the move that carries most boards.

1
Each X cell would make the 1 count more than 1.

The only way to reach the number

The 3 needs filled cells next to it, and the cell below it has an X. So its only way in is the cell to its right. Without that cell, the 3 could never reach its number, so it must be filled. On bigger boards look for these narrow spots: a cell that is the only bridge between a circle and the room it needs is filled.

3
The 3 can only reach its cells through its right-hand side.

Groups that join

Two separate groups near a circle can merge into one if you fill the cell between them, and then the circle counts the whole new group. That can push it past its number, but it can also be exactly what it needs. Each time you fill a cell, look at every circle its group touches and add up again.

Common mistakes

  • Counting cells instead of groups. A circle adds up the size of every filled group it touches, including cells that are far away but joined to them.
  • Counting a group twice. A group that touches a circle on two sides still counts once.
  • Filling a circle. Circles always stay empty, even the ones without a number.
  • Thinking it is Nurikabe. The filled cells do not need to be connected, and there is no rule about 2×2 blocks.

Questions and answers

What is Kurotto?

A Japanese logic puzzle where you fill cells around numbered circles. Each number is the total size of the filled groups touching its circle, each group counted once.

Is Kurotto the same as Kurodoko?

No. Kurodoko counts the cells a number can see along its row and column. Kurotto counts the sizes of the filled groups touching a circle.

What does an empty circle mean?

It stays empty itself, but it counts nothing: any number of filled cells may touch it.

How do I fill a cell or mark it empty?

Tap a cell to fill it, and tap again to clear it. Press and hold to mark it empty with an X. Drag to mark several cells in one stroke.

Where should I start?

With the 0s, then with circles that have only a little room around them. After that, check every free cell next to a group: would filling it make a circle count too much?

Ready to play?

Count whole groups, X the cells that would overshoot, and fill the only way in. That is how every Kurotto falls into place.