From which of the options, six pieces of shape S can be cut?
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For "can it be cut" or tiling problems, first do a quick area check. If the area is sufficient, try to visually tile the shape. Start by placing pieces along the edges and work inwards. Be aware that some configurations, especially those with holes, can have tricky constraints.
Option A: Removing one edge square leaves 24 cells that split evenly into six S-shaped pieces, so this works.
Option B: Removing a 2x2 corner leaves 21 cells that also divide cleanly into six pieces, so this works.
Option C: Removing one square from this particular edge leaves 24 cells, but the position of the missing square blocks a clean split into six pieces, so this does not work.
Option D: Removing the 2x2 corner block here leaves 21 cells that divide into six pieces the same way as option B, so this works.
A, B, and D work; C does not.
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Approach Solution -2
A third way to check this is to try to actually partition each shape into six non-overlapping copies of S by working outward from the removed square, since a clean partition existing is the real test, not just matching the total area.
Option A: Starting from the gap on the top edge, the remaining cells can be grouped, row by row, into six complete S-shaped blocks with nothing left over, so a partition exists.
Option B: Starting from the missing 2x2 corner, the rest of the grid splits into six S-shaped blocks that tile around that corner cleanly, so a partition exists.
Option C: Starting from the gap on the bottom edge, every way of grouping the remaining cells into six-piece blocks leaves at least one leftover cell that cannot join a full S shape, so no complete partition exists here.
Option D: Starting from its missing 2x2 corner, the same block-by-block grouping used for option B works here as well, giving six complete pieces.
Trying to build the actual partition confirms A, B, and D succeed while C leaves a stray cell behind.
