How to Solve Kin-Kon-Kan Puzzles

Though of uncertain origin, Kin-Kon-Kan has been featured in puzzle magazines such as the Japanese publication Nikoli. Your goal is to place a series of mirrors in the grid.

Each region has exactly 1 diagonal mirror, placed in a single cell.
Letter-number combinations project a laser beam into the grid, that much reach the matching letter by bouncing off a number of mirrors equal to the number in the pair.
Each mirror must reflect at least 1 beam
Beam lines are allowed to cross each other.

If at all possible, the best first step is to start with the clues that will only reflect their beam one time.

The mirror can only go in one possible cell, where the column and row of these clues intersects. Simply place the mirrors here, and we will have eliminated those regions from consideration for later clues.

Next, we’ll take a look at the D2 clues. They are both on the same side of the grid, and because there will only be two reflections, we know they have to basically make a U-turn.

At the bottom of the grid, we’ve filled in almost the entire row and there can’t be another mirror in those regions, which leave us only the cell in the middle to reflect the beam upwards.

Then, we only have to place a mirror in the single cell that’s able to send it back to the other D2.

Now let’s look at the E2 clues. Going up, you see that one beam must reflect off this mirror in front of the C1 clue, because there is no other region where a mirror could be placed in the path before it.

Since the beam can only reflect twice, that means we only need to place one mirror, and by simply looking down from the top E2 clue, we can see where the beams would intersect, so this must be where the mirror goes.

From here, things start getting tricky. We can see that both the A2 pair and the G2 pair have to make a U-turn in adjacent cells. Since these cells must be in separate regions (one mirror per region, remember?), and can’t block line of sight for any of the beams we already solved, these are the possible mirror positions remaining for them.

Looking at the second option for the G2 mirror pair, we find that it can’t be placed. If it were, its angle would force the beam from the A2 on the left to go in the wrong direction, and because of the shape of the region, you could not place both the upper #2 G2 mirror, and the left #1 A2 mirror – they would be in the same region. Therefore, we know that the 1st position for the G2 mirrors is correct.

After placing the mirrors for the G2 pair, let’s look at the options for A2.

If we choose the second pair placement, we would use both of the blue highlighted regions. From there, notice the beam direction from B3. If no mirror is placed, the beam leaves the grid.

If it’s placed in the position marked 1 in the remaining white region, it would block the beam from the A2 pair. So the only possible cell to place a mirror is the one highlighted in red.

If slanted one way, it would reflect the beam up and out of the grid. If it’s the other way, it would hit the highlighted mirror and also leave the grid.

Since that eliminates all options with mirror pair #2 for A2, then the correct position must be #1, right next to the grid edge.

Only one region left, so only one mirror to place.

If we look at the beams from the two B3 clues, we see they will reflect from the highlighted mirrors.

The cell highlighted in red is where these reflected beams would intersect, so that must be where our final mirror goes, which will reflect the beam a total of 3 times, as the clue requires.