Solving GraphiLogic Puzzles
The table side
A set cell at (or near) the table border is a quick winner. If you found a cell on any side of the table, make
sure to check the corresponding rule, and fill the whole block (and clear the following gap):
Mark the incomplete blocks
Most of the cases you will not be able to identify the exact position of a block, but quite often you will be
able to draw its limits to an extent. Whenever you can refine the position of a block, mark it on the grid.
A block of 5 cells must occupy the middle region of an 8 cell space:
A block of 3 cells, which contains a known cell, can not reach distant cells. Also, this block is too big to
fit to the left of the known cell, so it will occupy at least one cell to the right, too.
In this case, neither of the 2-cell blocks could reach the center, and the block on the right side can not reach the rightmost cell:
Count, count, count
Spotting a block which occupies the whole line (row or column) is obvious. But most of the time, your solution won't be
that easy. Usually you've got to calculate: add all the block sizes in a given line, plus add 1 cell between the
blocks. If the sum is equal to the length of the available space, you won. But even if it is less, you might still
earn a few cells.
A block of 3 cells and a block of 4 cells fills entirely a 8-cell space (as there need to be at least 1 cell of gap between):
Note: in the case of Color GraphiLogic tables, block of different colors can touch, thus you can only count on
the gap cell for adjacent blocks of the same color.
Two blocks of 3 cells (and the gap cell between them) occupies some of the cells, for sure:
In fact, determining if a block has a fixed cell is quite simple:
- Calculate the sum: add all the sizes of the blocks, and the gap cells between.
- Now, if adding the size of the biggest block to the sum gives a number greater than the space available, then
we have fixed cell(s). If you subtract the available space from the given number, the result even tells you the
number of fixed cells of the biggest block.
With the above example (two 3-cell blocks and the gap between):
- sum: 3+1+3 = 7
- space: 8
- the biggest block is 3-cell: 7+3 = 10, it's greater than the available space (of 8) by 2, thus the 3-cell block has 2 fixed cells.
Another example of 1+1+3 blocks (and the gaps between):
- sum: 1+1+1+1+3 = 7
- space: 8
- the single block: 7+1 = 8, which is not greater than the available space, so no fixed block.
- the biggest (3-cell) block: 7+3 = 10, which is greater than the space by 2, so it has 2 fixed cells.
Determining where the fixed blocks are is a bit more tricky: you have to count the blocks and gaps from left to right,
remembering the block positions, which will give you the leftmost positions of each blocks. After finished, you
have to count the blocks from right to left, which gives you the rightmost position of each blocks. The fixed cells
are the ones that are overlapped by the leftmost and rightmost position of any given blocks. (Don't panic, the
drawing will help with it :) )
A single blocks fixed cells can also be determined by this left-right method:
The method works just fine with more complex cases, but be aware that only those cells are fixed, where the very
same block overlaps itself:
Note: no more of the above cells are fixed, as the 3rd, 6th and 14th cells are overlaps of different blocks.
There is no overlapping between the same blocks (the overlapping at the middle is between two different
blocks), so we found no fixed cells here:
Known empty cells make a huge difference, when counting:
Known set cells can help, too:
Note: the 3-cell block could not start at the leftmost cell, because there is no room left for a gap (so it would
touch the pre-known set cell, which would make it 4-cell long)