Rules and how to solve Heyawake.
Rules
  1. Arrange the black cells so that they do not line up vertically and horizontally in some of the cells on the board.
  2. If there is a problem number in a group of rectangular cells surrounded by a thick border, the same number of black cells will be placed in that group. For groups without numbers, there can be any number of black cells.
  3. White cells connected vertically and horizontally must not span three groups.
  4. The board must not be divided by black cells. (All white cells are connected vertically and horizontally.)


jump to Heyawake problem.
Tips for solving
解くポイントはまず数字のあるグループでグループの形と数字で一意に黒枡位置が決まるところに注目します。例えば1×3のグループで2の指定がある、 3×3のグループで5の指定があるなどです。数字が0のグループも全枡白桝に決まります。
次は辺や角で同じ様にグル-プの形と数字で黒枡が決まるところに注目です。例えば辺にある3×2(辺に接するのは3)で3、角の2×2で2などです。
その後は黒枡の隣枡が白桝に決まったり、黒枡による分断が起きないように白桝に決まったりするところを白桝にします。 するとグループの未定の枡が上の手法で決まる枡が出てきます。
白黒未定の枡をすべて黒枡にすると問題数字の黒枡数になる時も黒枡に決定できます。
あとは白桝が3グループにならないように黒枡にする、黒枡で分断されないように白桝にしていくように進めます。
The point to be solved is to focus on a group with numbers, where the shape of the group and the number determine the position of the black basin uniquely. For example, a 1 × 3 group has 2 designations, a 3 × 3 group has 5 designations, etc. In a group with a number of 0,all cells are also determined as a white cells.
Next, it is noteworthy that the shape of the group and the number determine the black cells in the same way on the sides and corners. For example, a group with problem cell 3 specified by 3 x 2 on the side (3 in contact with the side), a group with problem cell 2 specified by 2 x 2 on the corner, and so on.
After that, the place where the next cell of the black cell is decided to be a white cell or the place where it is decided to be a white cell so as not to be divided by the black cell will be a white cell. Then, there will be a cell whose group is determined by the above method.
If all the black and white undetermined cells are changed to black cells, the number of black cells in the problem figure can be just determined as black cells.
After that, we will make the black cells so that the white cells will not be connected to the three groups, and the white cells so that they are not divided by the black cells.
Let me explain with a real problem. The following figure is the problem.
For easier understanding, black and white undetermined cells are shown in gray, but in practice, black and white cells are generally displayed.
ex0
First, in the group of 0 with a light blue frame on the upper right, it is determined as all white celles.
In the 3x2 group of the yellow-green frame on the upper left, the yellow-green frame is a black cell. If the yellow-green frame are white cells and the remaining cells are black, the black cells make separate them.
In a 2x2 cell with a blue cell at the bottom right, if the cell with the blue cells re not a black cells, it will be divided by the black cells.
If the position of the specified number of black cell is determined, the other cell in the same group will be white.
ex1
The cell next to the cell where the black square is determined is white, the cell with the light blue frame is the white cell in this figure . In addition, the blue frame is also determined as the white cell so that the black square does not separate. ex2
Next, consider the group of number 1 with a yellow-green frame at the left end. In this group, the only black-and-white undetermined cell is this with a yellow-green frame. Unless this cell is a black cell, the specified one black cell cannot be placed. The cell with a yellow-green frame is a black cell. The next cell next to the black cell will be a white cell.
If the green frame is not a black square, three groups of white cells from the left side will be continuous. If the green frame becomes a black cell, the black cell with the specified problem number has been placed, so the remaining cells in the same group will be white cells.
ex3
Next, considering the group of problem number 2 with a light blue frame and a blue frame, one white cell was decided on the left end, so the remaining cells were exactly two black cells.
The cells in the light blue frame become black cells and the remaining cells in the blue frame become white cells. Other cells next to the black cell will also be white cells.
ex4
The blue frame is black so that the white cells are not continuous in three groups.
The yellow-green frame is a white cell so that the black cells does not separate the board.
The green framed cell next to the black cell also becomes a white cell.
ex5
In the group of problem number 2 in the lower left, three cells becom white, so two black cells fit in the remaining three cells.
The yellow-green frame is a black cell, and the blue frame next to the black cell is a white cell.
ex6
This is the correct solution. ex7
The following are some tips.
First, an example where a black cell is uniquely determined from the group shape and the question numbers. Includes what is determined when it is on the side or corner. It is good to consider how it is decided.
It is not a solvable problem because it is a diagram for explanation.
ex10
Some are determined by a combination of multiple groups. ex10
Consider the group with a yellow-green frame and a blue frame at the top of the following figure. When trying to put three black cells, it is either three cells of yellow-green frame or three cells of blue, but if the yellow-green frame are changed to black, the black cells will break the board. Therefore, a blue frame is a black celland a yellow-green frame is a white celle.
Next, consider the lower left part. If one of the cells in the yellow frame does not become a black cell, it will become white cells for three consecutive groups. With this in mind, considering the group of light blue frame and green frame, if the cell of the light blue frame is a black one, then either the yellow frame will be a black one, and the board surface will be divided to two by the black cells. Therefore, here, the green frame is a black cell and the light blue frame is a white cell.
Finally, consider the red frame. If this cell is a black cell, the pink cell will be a white cell and become white cells for three consecutive groups, so the red cell will be a white cell.
There are various other patterns, so it is better to learn while solving the problem.
ex11



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