Hole Punching
Unfold the paper and place every hole.
Hole Punching presents a square sheet of paper that is folded one or more times (shown step by step). A single hole is then punched through the folded stack. Your task is to determine exactly where all the holes appear when the paper is completely unfolded, choosing the correct pattern on a 4×4 grid of sixteen squares.
Also known as: Paper Folding, Hole Punches, DAT Hole Punching
Pick an answer above, then check it.
How Hole Punching works on the DAT
- 1
You watch the paper get folded one or more times.
- 2
A hole is punched through all the folded layers at once.
- 3
You mentally unfold the paper, reflecting holes across each fold line.
- 4
You select the resulting hole pattern on the 4×4 grid.
Why students struggle
- Tracking multiple folds in the right order.
- Reflecting holes across the correct fold line (mirror axis).
- Knowing how many layers the punch went through.
- Diagonal folds that reflect across a slanted axis.
Common mistakes to avoid
- Mirroring a hole across the wrong fold line.
- Forgetting one of the folds entirely.
- Ending with the wrong number of holes.
- Unfolding in the order the paper was folded instead of reverse.
Proven strategies for Hole Punching
The tactics our highest-scoring students use to speed through Hole Punching without losing accuracy.
1. Unfold in reverse order
Undo the last fold first. Each time you unfold, every existing hole is mirrored across that fold line. Working backwards keeps the mirroring straight.
2. Layers = number of holes
Count how many layers of paper the punch passed through — that's exactly how many holes you'll end up with. It's a fast sanity check against the answers.
3. Treat fold lines as mirrors
Every fold line is an axis of reflection. Place a hole, then drop its mirror image across each fold line you reverse.
4. Use the grid coordinates
Name the punched square by its row and column, then reflect those coordinates across each fold line rather than eyeballing positions.
How PATCrusher helps you master Hole Punching
Animated fold/unfold generator
Practice unlimited hole-punching problems where you can watch the fold sequence and the unfolding play out.
Step-by-step unfolding solutions
Each explanation unfolds the paper one fold at a time on the grid, showing how every hole mirrors into place.
Master the other PAT sections
Further reading on Hole Punching
Hole Punching — frequently asked questions
Quick answers about the DAT PAT Hole Punching section.
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