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What a Fold Does to Layers
The Punch Goes Through Every Layer
Summary
The punch goes all the way down
The punch is not a mark on the top sheet. It drives through the entire stack sitting under it, so every original square in that stack comes away with a hole in it — and every one of those squares shows up on the answer grid.
One half fold, one punch, two holes. The stack under the punch was two squares deep, so two squares were pierced.
The answer grid is the flat sheet, not the folded one
Look at where those two holes landed. The punch went through a spot on the left side of the folded paper, but the answer grid shows holes at the far left and the far right of that row. The right-hand square was the one lying underneath the punch when the fold brought it there; unfolded, it goes home and takes its hole with it.
The grid is never a picture of the folded paper. It is the original square, sixteen positions, with a filled circle at every original square the punch went through.
That is the same folded state as layer counts, and the punched position reads 2. Two layers, two holes. You did not need to know where the holes would land to know how many there would be.
Every layer at that spot — and only that spot
The count belongs to the position you punch, not to the sheet as a whole. Fold a quarter fold and then a half fold and the covered paper is four deep in one column and two deep in the next:
Punch the column reading 4 and the punch takes four squares with it:
Four holes, in a 2×2 block on the left of the sheet. Had the punch landed one column to the right — same paper, same folds, same everything — it would have found a stack two deep and produced two holes. The punch collects whatever is under it at that one spot.
Where a punch is allowed to land
Two conditions have to hold. The paper under the punch must be complete: the position fully covered, no bare gap under the hole. And the paper there must never have been split by a crease.
This sheet has one center fold, creased down the middle of the second column. The paper's edge stops halfway across that column, so those positions are only half covered — and the squares there have been folded onto themselves. Both conditions fail. Only the two right-hand columns are punchable here, and the punch above sits in one of them.
A creased square stays out of play permanently. Once a fold has split it, it is excluded wherever later folds carry it, even if nothing creases it again. The reason is practical: a punch through a half-covered or creased square would unfold into a partial hole or one sitting off the sixteen positions, and the answer grid has no way to draw either.
One punch per item
Practice items punch exactly one position — one spot, at every difficulty. That single fact is what turns the pierce rule into arithmetic you can use: with one punch, the number of holes in the correct answer is simply the number of layers stacked under it.
2 folds, then 1 punch through 4 layers — 4 holes appear when unfolded. Unfold in reverse order: each fold mirrors its holes across the crease.
The item's own explanation says it outright: one punch through four layers, four holes when unfolded. Where those four holes sit is the next lesson's job.
The takeaway
A punch pierces the whole stack beneath it, and each pierced square becomes a filled circle at its own original position on the answer grid — not at the position you punched. A punch may only land where the paper is complete and uncreased, so crease bands are permanently out of play. Because every item punches exactly one spot, the hole count of the correct answer equals the layer count at that spot.
Practice Questions
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