Block Puzzle

Block Puzzle Example

Block Puzzle is a variation of a puzzle genre made by nikoli. I encounter this variation in mathgrant’s blog.

Cell types

All cells have a symbol (usually letters, but can be anything from digits, letters, numbers, symbols, or even some pictures) in each. The objective is to divide the grid into several regions to satisfy the requirements below the grid.

Interaction

First, we will assume that all symbols are letters, for ease of explaining. Below the grid, there exist some words (or strings of letters, though usually I make them to have meanings) and some numbers. Each of these words must appear in the grid exactly as much as the number states. In the example, the word “CALL” must appear four times. Note that the letters may be scrambled.

Objective

Divide the grid into several regions such that each region satisfy a group below the grid, and all groups below the grid are represented in the grid.

Walkthrough of the example

Note that C and A only appears once in each group, so we can draw some borders. Soon, we will get that R1C2, R2C2, and R2C3 form a group (with missing one more), and this group is separate from R1C3. So R1C3 must go to R1C4, R2C4, and R3C4 to form a group of 4; the letters are automatically satisfied.

R1C1, R2C1, and R3C1 also form a group, missing an L. The only L around the group is R4C1, so they form a group.

Similarly, R1C2, R2C2, and R2C3 are missing an L, which can be found at R3C3. The rest automatically forms a group.

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