PUZZLE EDITING

by Zack Butler

Solution: CABARET

Directions for all puzzle types can be found at http://www.nikoli.co.jp/en/puzzles, except for Edel, which is a paint by numbers. Most of these puzzles have areas of non-uniqueness. The key is to determine how many possible solution grids each puzzle has.

Fillomino

1 4 4 4 8 8 3 7 5 5 5 3 6
2 4 1 8 8 3 3 7 4 5 5 3 6
2 1 5 3 8 7 7 7 4 4 4 3 6
1 2 5 3 8 3 7 3 3 1 3 6 6
6 2 5 3 8 3 7 3 4 4 3 3 6
6 6 5 5 8 3 1 4 4 2 4 4 4
7 6 6 6 5 5 2 2 3 2 3 3 4
7 7 7 2 5 8 8 10 3 3 1 3 1
4 2 7 2 5 8 2 10 10 10 4 4 4
4 2 7 7 5 8 2 5 10 10 2 2 4
4 4 8 8 8 8 5 5 10 5 5 5 2
3 2 1 2 2 5 2 10 10 1 5 2
2 3 3 3 5 2 10 2 2 5 1

In the lower left 2x2, we need three 3s (and therefore a 1) - any of the unfilled squares can be the 1 so we have 3 solutions.

Nurikabe

4
3 2 3
4 5
1 6
12 6 6
3 3
2 3
6 4
1 3

Only 1 solution.

Masyu

There are two solutions in the bottom right - the white circle one from the corner can be traversed either vertically or horizontally, one way to finish the loop in each case, 2 solutions total.

Light Up

*
* * 0 *
* 2 * 3 * 4 *
* *
* 1 *
1 * 1 * 2
*
2 * *
* 2 *
*
* 0 * 1 0 *
0 * 2 *
*

Only 1 solution.

Heyawake

3 2 2
3 2
0 3
2
3 3
4 0
1
2 2

In the upper left and lower right, one or neither of the two grey squares can be filled in, 3 options in each place. In the lower left, exactly one of the two must be filled in, 2 options. These are independent, so 3x3x2=18 solutions.

Hitori

4 6 1 2 5 3 11 10 9 4 4 4 1
5 10 6 9 2 3 7 8 4 13 12 11 7
1 1 1 5 10 3 2 4 6 8 7 3 9
3 4 7 9 8 1 5 10 13 6 6 6 12
4 8 1 8 5 6 10 12 13 9 7 2 10
7 8 12 9 6 4 4 5 11 3 1 10 13
2 2 2 10 4 13 9 1 11 11 7 13 5
10 7 5 9 11 12 8 6 4 6 3 1 1
6 13 3 3 3 5 1 7 2 2 7 9 8
6 3 11 4 1 9 7 13 10 7 8 5 2
6 9 8 9 7 11 3 2 12 4 11 5 11
2 5 9 13 12 10 6 11 8 12 9 5 4
9 7 4 12 9 8 3 11 3 1 2 10 12

All unblackened squares must be white except for the four 9s in the fourth column, they may all be black or any one left white, for 5 solutions total.

Edel

1
1 1 1 2 1 1
1 1 1 1 1 1 1 1 1 1
1 2 12 2 1 1 1 1 2 1 1 1 8
1
7
1 6
1 1
1 1 1
1 1 1 1
1 1 1 1
1 1
7 1
1 5
1
3
2 2

For the grey squares, the remaining bits are one 1 in each column, one 1 in the top row, and two 1s in the other two rows. For each of the 5 spots the top 1 can go, there are four ways to put the other four 1s, for 20 total solutions.

The number of solutions are 3-1-2-1-18-5-20, and converting to letters gives CABARET.