Fold and Punch

You get given a square piece of paper. It gets folded, then a hole is punched straight through all the layers. Your job is to picture what the paper looks like when you open it back out flat.

The difficult questions use more than one fold. You will be shown a series of pictures, each one showing a fold. You have to follow those folds and work out where the holes will appear when the paper is opened out.

The method

Six beats: imagine the folds, focus on the holes, work backwards, mirror every hole, repeat for every fold, match and check.

1. Imagine the folds. Follow the pictures and imagine the paper being folded over. Look at where each folded piece lands. The paper is not always folded in half — it might be that only part of it folds over, like one edge or one corner.
2. Focus on the holes. The last picture shows where the holes are punched. For each one, ask whether it is on a part of the paper that has been folded over, or on a part that is still a single layer.
3. Work backwards. Start with the fold that was made last and open that one first. Never open everything at once.
4. Mirror every hole. As you open that fold, each hole on the folded part copies across to the other side of the crease — the same distance out, like a mirror image.
5. Repeat for every fold. Move on to the next fold and do the same again, this time including the new holes you have just made. Keep going until you are back to the original square.
6. Match and check. Find the option that matches the holes you have imagined. If you are still unsure, count: a hole on a part folded once leaves two holes, folded twice leaves four, folded three times leaves eight — counting the original hole each time.

About 25 to 35 seconds each. A one-fold question takes 12, so bank that time for the three-fold ones.

Watch out — the tricky ones

1. Lots of folds. More folds means more mirroring, and more holes. Take them one at a time and undo them in the right order. Jumping straight to the finished square is where most mistakes start.
2. Only part of the paper is folded. If a hole is on a part with just one layer, there is no mirror hole. It stays on its own. Always check the hole really was on a folded part.
3. Shaped holes. The hole might be a triangle, a heart, a star or a D. It gets mirrored across the crease just like a round one does, but because it is a mirror image the copy comes back the other way round — a D facing right returns facing left. Watch the direction, not just the position.

Try these yourself

Now have a go yourself — tap the square that shows the paper unfolded.

Related

• The complete 11+ question-type guide
• Hidden Shapes — the other question type GL prints in its own booklets
• Folding — the same crease-as-mirror idea, on a whole shape

All example questions come from the Brainblox question bank — practise this question type inside 21 arcade games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.