TACHS: Paper folding: two folds the same way
Learn to undo two parallel folds, the quarter-width crease first and the center crease second, so the four holes land at their true, uneven spacing.
Where do the holes go when a sheet is folded in half and then in half again in the same direction?
Short answer
Undo the second fold first by flipping across the quarter-width crease, then flip every hole across the center crease. The height never changes, and the holes come out in close pairs with wider gaps between.
Know first: Unfolding a single vertical fold, Counting columns from a line
Step 1 of 5
Two parallel creases, two different mirrors
Sometimes a sheet is folded in half, and then the folded strip is folded in half again the same way. Both creases run up and down, so they are parallel. The strip is a quarter of the full width and four layers thick, so one punch makes four holes, all at the same height.
The holes come from two different mirrors: first the quarter-width crease, then the center crease. That usually leaves them in close pairs with a wider gap between.
| Crease | Pairs of columns that match |
|---|---|
| Quarter crease, between columns 2 and 3 (undo first) | 1 and 4, 2 and 3 |
| Center crease, between columns 4 and 5 (undo second) | 1 and 8, 2 and 7, 3 and 6, 4 and 5 |
Each pair sits the same distance from its crease. For folds going left to right, the quarter crease is between columns 6 and 7, pairing 5 and 8, 6 and 7.
Step 2 of 5
Unfold the quarter crease first
Worked example: A punch next to the quarter crease
A sheet is 8 columns wide and 4 rows tall. First the right half folds over onto the left half (crease between columns 4 and 5). Then the right half of that strip folds over onto its left half (crease between columns 2 and 3), leaving columns 1 and 2. A hole is punched in row 1, column 2. Which picture shows the opened sheet?
- ARow 1: columns 2, 4, 6, 8
- BRow 1: columns 2, 3
- CRow 1: columns 2, 3, 6, 7
- DRow 1: columns 2, 7
- ERow 4: columns 2, 3, 6, 7
- 1
Undo the second fold
The quarter crease is between columns 2 and 3. Column 2 is 1 column left of it, so its partner is 1 column right: column 3. Holes so far: columns 2 and 3.
- 2
Undo the first fold
The center crease is between columns 4 and 5. Column 3 is 2 columns left of it, so its partner is column 6. Column 2 is 3 columns left, so its partner is column 7. Holes: columns 2, 3, 6 and 7.
- 3
Keep the height
Vertical creases only change left and right. All four holes stay in row 1.
- 4
See why the other choices are there
Columns 2, 4, 6, 8 spaces the holes evenly, which is what sliding the flaps instead of flipping them gives. Columns 2 and 3 undoes only the second fold. Columns 2 and 7 undoes only the first fold. Row 4, columns 2, 3, 6, 7 has the right columns at the wrong height.
Answer
Four holes in row 1, at columns 2, 3, 6 and 7.
| Col 1 | Col 2 | Col 3 | Col 4 | Col 5 | Col 6 | Col 7 | Col 8 | |
|---|---|---|---|---|---|---|---|---|
| Row 1 | · | hole | hole | · | · | hole | hole | · |
| Row 2 | · | · | · | · | · | · | · | · |
| Row 3 | · | · | · | · | · | · | · | · |
| Row 4 | · | · | · | · | · | · | · | · |
Gaps of 1, 3 and 1 columns between neighbors. Two mirrors make uneven spacing.
Find the wrong step
Same folds as the worked example. A student unfolds a hole punched in column 2.
- 1
Notes the two creases: center between columns 4 and 5, quarter between columns 2 and 3.
- 2
Undoes the first fold first: column 2 is 3 columns left of the center crease, so the partner goes in column 7.
What went wrong
Folds come undone in reverse order. The center crease is buried inside the strip until the quarter fold is opened, so flipping across it first puts holes in the wrong places.
- 3
Then reflects column 7 across the quarter crease and lands off the edge of the sheet.
The fix
Undo the last fold first. Column 2 flips to column 3 across the quarter crease, then columns 2 and 3 flip to 7 and 6 across the center crease.
Step 3 of 5
Undo parallel folds on your own
Check yourself · Question 1
A sheet 8 columns wide is folded left to right twice: first across the center (between columns 4 and 5), then across the middle of the strip (between columns 6 and 7), leaving columns 7 and 8. A hole is punched in column 8. After you undo only the second fold, which columns have holes?
Answer: B
The second crease is between columns 6 and 7. Column 8 is 2 columns right of it, so its partner is 2 columns left of it: column 5.
Check yourself · Question 2
Same folds as the last question: left to right twice, leaving columns 7 and 8. Two holes are punched: row 1, column 7 and row 4, column 8. Which picture shows the opened sheet?
Answer: D
Row 1: column 7 flips to 6 across the quarter crease, then 7 and 6 flip to 2 and 3 across the center. Row 4: column 8 flips to 5, then 8 and 5 flip to 1 and 4. Each row keeps its own holes.
Trap answer: Row 1: columns 1, 3, 5, 7. Row 4: columns 2, 4, 6, 8.
Evenly spaced holes
- Why it looks right
- Even spacing looks tidy, and it has the right number of holes in each row.
- Why it's wrong
- Each hole is measured from a crease, and the two creases are in different places. That makes close pairs with wider gaps.
- The right answer
- Row 1: columns 2, 3, 6, 7. Row 4: columns 1, 4, 5, 8.
Common mistake
I put the second crease in the middle of the sheet.
- Why it's tempting
- The first crease was in the middle, so the second one feels like it should be too.
- Do this instead
- The second fold halves the strip, not the sheet. Its crease is a quarter of the way in from the edge.
Step 4 of 5
What to remember
Remember
- Two parallel folds make four layers, so one punch makes four holes at the same height.
- Undo the quarter-width crease first, then the center crease, flipping every hole each time.
- Expect close pairs with wider gaps. Evenly spaced holes are the classic wrong picture.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
Try another one
In your own words
In the practice question, which column was the punch in, and which columns did each undo add?