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Walkthroughs and Pacing
Worked Walkthroughs
Summary
Three real items, solved end to end. Nothing new appears here — only the order you already have: read the panels, count the layers under the punch, unfold backward, verify. Rows and columns are numbered 1 to 4 from the top left throughout.
Item 1 — two creases, three holes
The paper is folded as shown, then punched through all layers. Which pattern shows the holes on the fully unfolded sheet?
Read the panels before you look at a single answer grid. In the first panel the paper fills the left three columns, so the crease ran down the line between columns 3 and 4 and the last column folded left onto column 3. In the second the paper fills the right two columns: the crease is the line between columns 2 and 3, and columns 1 and 2 have swung right onto columns 4 and 3. That fold lands partly on paper the first one had vacated, which is legal — the sheet never leaves the dashed square.
The punch is the small open circle on the last panel, in the top row, column 3. Note it first. It is the one thing unfolding destroys.
Count the layers
Column 3 carried two layers after the first fold — itself and the column off the right edge. The second fold laid column 2 on top, making three. Three layers means three holes, and you know that before you know where any of them sit.
Now run the count down the answer grids. D shows one hole, and a single hole never wins: it would mean the punch found paper one layer thick, and these items are built so it pierces at least two. C shows six and E shows four — both claim more holes than there are layers to pierce. Three options gone, and you have not judged a position yet.
Place the holes
A and B both show three holes, so position decides. Both creases here are vertical, which means no fold in this item could move a hole out of its row. The punch sits in the top row, so all three holes sit in the top row. A puts its three in row 2. B is the answer.
Unfold backward to confirm, last fold first. Undo the crease between columns 2 and 3: the hole at column 3 mirrors to column 2. Undo the crease between columns 3 and 4: the hole at column 3 mirrors to column 4, while the column-2 hole's mirror would land outside the original square, so it has no partner. Top row, columns 2, 3 and 4 — three holes, exactly as counted.
2 folds, then 1 punch through 3 layers — 3 holes appear when unfolded. Unfold in reverse order: each fold mirrors its holes across the crease.
Item 2 — a crease that ignores the grid lines
The paper is folded as shown, then punched through all layers. Which pattern shows the holes on the fully unfolded sheet?
The first panel's left edge does not sit on a grid line: it runs down the middle of column 2. The strip left of that crease folded right, landing one full cell past it, so column 1 now lies on column 3. The second panel keeps the same ragged left edge and loses the bottom half, so the second crease is the line between rows 2 and 3. The punch is again in the top row, column 3.
Count the layers
Column 3 holds two layers after the first fold, and the second fold doubles everything it covers. Four layers, four holes.
The count kills three again. B shows two and E shows three — too few. D shows eight, filling the top and bottom rows completely: the most symmetrical grid in the row, and twice the answer's size. Symmetry is evidence of nothing, and eight holes cannot come out of four layers.
Place the holes
A and C both show four holes, two in the top row and two in the bottom, so position decides again. The horizontal crease pairs row 1 with row 4, which both respect. The vertical crease separates them: the punch sits in column 3, and a crease down the middle of column 2 sends column 3 to column 1. The holes belong in columns 1 and 3. A puts its pairs in columns 2 and 4. C is the answer.
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.
Item 3 — three folds, one of them diagonal
The paper is folded as shown, then punched through all layers. Which pattern shows the holes on the fully unfolded sheet?
Half the square is gone in the first panel: the paper is the triangle below the crease running corner to corner from top left to bottom right. A diagonal crease trades a position's row for its column, so whatever sat at row r, column c now sits at row c, column r. In the second panel the bottom row has folded up onto the row above, bringing a mirrored slice of that diagonal edge with it — the small sloped step on the right is the tell. In the third the top of the shape has folded down across the line between rows 2 and 3, back over the space the second fold emptied. The punch sits in row 3, column 1.
Count the layers
Track the stack under that cell as you read, not afterward: two layers after the diagonal, four once the bottom row comes up onto it, six once the top comes down. Six layers, six holes.
B shows ten — the whole top row, the whole bottom row and the whole left column. It is the tidiest grid in the row and it is four more holes than the paper has layers to give. A and D show five: one short, which is what forgetting a single layer looks like. That leaves C and E.
Place the holes
Both survivors are the same L: three holes along a row, three down a column. Unfold backward. Undo the last crease, between rows 2 and 3, and the punch in row 3 mirrors to row 2. Undo the crease between rows 3 and 4, and the row-3 hole mirrors to row 4 — the row-2 hole's mirror would leave the square, so it gets none. Column 1 now carries rows 2, 3 and 4, and pointedly not row 1. Undo the diagonal and those three swap row for column, landing in row 1 at columns 2, 3 and 4.
So a corner decides it. The finished pattern leaves the top-left position open and fills the bottom-left one. C does that. E is the identical L with those two corners exchanged — the answer flipped top for bottom, right count, right shape, wrong sheet. C is the answer.
3 folds, then 1 punch through 6 layers — 6 holes appear when unfolded. Unfold in reverse order: each fold mirrors its holes across the crease.
Say the solve out loud
None of that was clever. It was four sentences in the same order, three times: here are the creases, here is the punch, here is the layer count, here is where the mirrors put them. It works because each sentence was finished before the next one started.
So make it audible in review, on the items you got right as well. Where you stall is the step you have not automated: name the creases but not the layer count and your counting is the bottleneck; count fine but keep landing on the wrong row and your mirrors are. A right answer you cannot narrate is a miss you have not had yet.
The takeaway
Read the panels and fix the punch position first, because the punch is the one thing unfolding destroys. Count the layers next: it costs no positions and it eliminated three of five options in every item above. Then place the holes by mirroring backward, last fold first, and let one landmark position settle the survivors. Difficulty adds folds and layers, never a new step.
Practice Questions
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