Punched Hole Pattern Questions: The JNVST MAT Type That Rewards Patience

What's Being Asked

A punched hole pattern question shows a square piece of paper folded one or more times, with a hole punched through it at a specific spot after folding, and asks what the paper looks like once fully unfolded — how many holes there are and where. It's one of the harder MAT question types because it asks a student to reverse a physical process entirely in her head, tracking every fold and every layer the hole punch actually passed through.

A Worked Example

Take a square folded in half once, left edge to right edge, and then punched once near the folded edge. Unfolded, that single punch becomes two holes, mirrored across the vertical center line where the fold was — because the punch went through both layers of paper at once. Now add a second fold: the same square folded left-to-right and then top-to-bottom before punching once near the corner where all folds meet. That single punch now passes through four layers, so unfolding gives four holes, one in each quadrant, each positioned as the mirror image of the punch across both fold lines. Students who track only the first fold and forget the second consistently answer with two holes instead of four.

The Trap Students Fall Into

The most common mistake is trying to visualize the fully unfolded result in one jump instead of undoing one fold at a time. Skipping straight to the final picture works for simple one-fold questions but breaks down completely once there are two or three folds, because the position of a hole after undoing the first fold changes where it lands relative to the second fold line — the order of unfolding matters, and doing it in reverse, one step at a time, is the only reliable method.

How I'd Practice This

• Physically fold a square piece of paper, punch it, and unfold it yourself several times before trying to do this purely on paper in your head — there's no substitute for having actually seen the real result a few times
• When solving on paper, undo folds one at a time in reverse order, redrawing the hole's mirrored position after each single unfold rather than guessing the final pattern directly
• Pay attention to how many layers the punch actually went through — that number tells you exactly how many holes to expect before you even work out where they are

Why This One Needs Real Paper First

Of all the MAT question types, this is the one where I most insist a student handle actual folded paper before attempting it abstractly. The mental model only becomes reliable once the physical version has been seen enough times to trust.