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Daily CellBlocks

Monday 8th January 2018

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Cell Blocks puzzle solution
This is an example of a completed CellBlocks puzzle. The grid start with a set of number clues, and no rectangles. The aim of this puzzle is to split the grid up in to rectangles (squares are rectangles), so that each rectangle has a single clue inside it, and the number of cells in that rectangle matches the clue.
A CellBlock puzzle is also sometimes known as a Shikaku puzzle - they are the same type of puzzle, just a different name.
Cell Blocks puzzle
This is an example starting grid. Our aim is to fill the grid with rectangles, so that each rectangle contains just one clue, and each rectangle contains the number of cells given by the clue.
The best place to start a CellBlock puzzle is to look for clues that can only be expanded in one direction. I have highlighted two cells where this is the case. Look at the '6' clue in the top-left, this clue is surrounded by the outside of the puzzle and the '2' clue. The rectangle for the '6' clue can only be extend downwards.
The highlighted '2' clue in the bottom-left is also surrounded on 3 sides by the outside of the puzzle and other clues. The rectangle for this clue can only be extended to the left.
Cell Blocks puzzle
Another technique is to look for cells that can only be reached by one clue. Look at the highlighted cell marked by 'A', the only clue that can reach this cell is the '2' immediately above it. There are no other clues that can reach this cell - the '2' clue to the right already has it's rectangle of 2 cells, so this rectangle can't be extended any more. That means that the cell marked by 'A' and the '2' clue immediately above it form a rectangle.
We can make the same deduction about the cell marked by 'B', it can only be reached by the '2' clue immediately above it. The cell marked by 'B' and the 2 immediately above it form a rectangle.
We can make the same deduction about the cell marked by 'C', but this is a little more complicated. The only clue that can reach this cell is the '4' immediately to it's right. Further, you can form a rectangle with 4 clues with a 4x1, 1x4, or 2x2 arrangement. There isn't enough space to the left/right for a 4x1 arrangement, so this must be a 2x2 arrangement, i.e. the rectangle for the '4' clue is the clue itself, cell C and the two cells above them.
Cell Blocks puzzle
We can now look at the highlighted '3' in the top right. There are only two ways to arrange a rectangle with 3 cells, either by 1x3, or 3x1. There isn't enough space here for a 1x3 arrangement, so the arrangement must be 3x1, with the '3' clue in the center cell.
As we saw in the previous step, there are three ways to arrange a rectangle with 4 cell, 1x4, 4x1, or 2x2. Look at the highlighted '4' clue, there isn't enough space here for 1x4 or 4x1, so the arrangement must be 2x2 with the '4' clue itself in the top-right corner.
Cell Blocks puzzle
This opens a number of clues that we can now draw rectangles for,
  • The highlighted '4' clue on the top row is the only clue that can 'reach' the cell in the top-right of the puzzle, so this rectangle must be 4x1 with the '4' clue at the far-left end.
  • The highlighted '2' can only be extended downwards.
  • The highlighted empty cell can only be 'reached' by the '3' clue to it's left - the '4' clue can't reach as there isn't enough space for a 1x4 rectangle.
  • The highlighted '6' clue must form a 2x3 rectangle. The possible arrangements for a '6' clue area 1x6, 2x3, 3x2, or 6x1, there is only space here for a 2x3 rectangle.
Cell Blocks puzzle
We can now tackle the big '16' clue. There are many ways that a '16' clue can be arranged, let's look at each of them in turn,
  • 1x16: The puzzle isn't big enough for this.
  • 16x1: The puzzle isn't big enough for this.
  • 8x2: There isn't enough horizontal space for this - there is only enough space for 2x7.
  • 2x8: There isn't enough vertical space for this - there is only enough space for 2x6.
  • 4x4: This is the only arrangement that can fit. With all the other rectangles in place, there is also only one ways a 4x4 rectangle can fit as well - look at the next step to see what this arrangement is.
Cell Blocks puzzle
We can now look at the two '12' clues that are in this puzzle. The '12' clue in the middle of the grid can only be arranged as 2x6 to fit within the space available to it.
The '12' clue in the top-left can also only be arranged as 2x6 to fit within the space available to it.
Cell Blocks puzzle
We have now cracked this puzzle! You can now apply all of the techniques you have learnt to fill in the rest of this grid.
Cell Blocks puzzle
This is the completed puzzle! You now have all the techniques you need to tackle our CellBlocks puzzles. The smaller puzzles are easier, so start with those and then work up to the bigger puzzles.
CellBlocks is also known as Shikaku, so might see it called by different names in different places.

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