How to Solve Ichimaga Puzzles
Ichimaga seems to have first appeared in the Japanese puzzle magazine Nikoli. Your goal is to connect all the circles into a single group by darkening grid lines.
- Numbers in the circles indicate the number of lines that connect to it
- A line may take no more than one right turn between circles, and this must be at an intersection.
- Solution lines otherwise do not branch – intersections without circles will only have one line pass through them.
- All circles will form a single group – you can get from one circle to any other circle by following the lines.
The best way to begin an Ichimaga puzzle is to look for circles that have a number that matches the number of possible lines leading out from them. For example, this 4 must use all four possible lines leading away, so we can darken all of them.
Other good starting points are 2s in a corner, and 3s along the grid edges. Since the example puzzle has several of those, we’ll fill them in now.
After marking out the easy lines, we have one more quick move here at the bottom of the puzzle. This 2 already has one line connected to it, so it only gets one more. It can’t be connected to the 1 above it, because that would leave a line at the bottom just pointing at nothing.
So this 2 must be connected to the 3 in the bottom row.
Next, we’re going to look at this line on the bottom right. Because it’s in the corner of the grid, it’s going to have to turn upward.
A line is only allowed to make one right turn, so that means it must connect to the 2 directly above it.
Looking at this 1, we already know that it can’t connect to the 2 below it. If it went up one space and turned right to connect to the 2 on the right side of the puzzle, it would isolate all the numbers at the top of the grid, so that’s not correct.
It also can’t simply go up two spaces and connect to the 2 at the top of the grid, because that would also create a group isolated from the rest of the numbers.
This means it must connect to the 4.
Now we’re going to consider this line. From its current endpoint, it can’t turn left or right, because that would create a branch in a non-clue intersection, which is not allowed.
If we extend it as far as the red dot, it still can’t turn left or right for the same reason.
At the green dot, it can’t turn left, because it would have to make a second turn to connect to a number, which it is not permitted to do. Turning right is also out, because not only would it be odd to connect the same pair of numbers together with two separate lines, but it would also use the last connection to that 2, and isolate the other numbers in the puzzle.
So we know it has to extend at least as far as the blue dot.
And we can see that this 2 has to connect to the one above it, because that’s the only path left to it.
Then we look at the 2 on the top of the right side of the puzzle. Again, it can’t connect to the line we just extended, because that would cut off the other clues we still have to connect.
That means that the top 2 must go upward and connect to the 1 at the top of the grid, and the line has to turn left and connect to the other 2.
