Hole Punching (officially Paper Folding) shows a square sheet folded one to three times and then punched. You choose the pattern of holes you would see after unfolding it.
PAT Grind has 1,200 hole punching questions at three difficulty levels. Each one is checked by an independent solver and comes with a step-by-step explanation.
How the questions work
- Dashed lines show where the paper was before a fold, and solid lines show where it is now.
- The paper is never turned over or twisted, and the folded paper always stays within the original square.
- Holes can only appear in 16 positions, on a 4 by 4 grid.
Strategy
- Unfold in reverse order, starting from the last fold.
- Each time you undo a fold, every hole on the folded flap gets a mirror twin across the crease.
- Count the layers under each punch. Two layers give two holes, four layers give four.
- For diagonal folds, reflect across the diagonal: a hole's row and column swap places.
Common traps
- Forgetting one of the folds.
- Mirroring across the wrong crease.
- Missing a layer that only part of the punch goes through.