Today's puzzles require you to wrestle with a piece of paper.

This is the best way to learn a new subject. A recent study by psychologists concluded.

According to the report, activities that train spatial reasoning like paper folding, building with blocks, and solving three-dimensional puzzles are the most effective way for young people.

The report says that when children learn the relationship between space and shapes through puzzles, their mathematics performance improves. If you want to do spatial computer games, you should use your hands instead of a mouse.

Spatial reasoning training is more effective than other interventions such as summer school, chess clubs, and getting older kids to help younger ones.

Physical puzzles are neglected in educational practice and policy. Dr Gilligan-Lee thinks that increasing spatial training in the classroom could dramatically improve mathematics outcomes in the UK, which lags behind its international competitors.

Today's tasks. I hope you enjoy them as much as I did. It is satisfying to connect directly with an object without being influenced by writing on paper or thinking in abstract ideas.

You need a square sheet of paper for all the puzzles. You may need a hole punch or sharp object for the final puzzles.

1. The triangle folds.

A square paper should be folded in such a way that it marks an equilateral triangle. The ruler and compass are not allowed.

Paper puzzle

Illustration: The Paper Puzzle Book (World Scientific)

2. The shape is 3D.

Can you fold a square sheet of paper so that it becomes a closed 3D shape? Since you will create an overlap or extra flaps, you cannot fold the square to make a cube.

Hole punch puzzles.

If you punch a single hole through the folded paper, you will match the image when the paper is fully unfolded.

3. The X is what it is.

hole punch 1

To get you started.

4. The diagonal.

A little bit trickier

A little bit trickier

5. The ring has something on it.

hole punch 3.1

Harder still.

6. A hole punch.

This one is really tough!

This one is really tough!

I will be back at 5pm UK with the solutions. Discuss your favourite physical puzzles below the line.

The Paper Puzzle Book and the Two-Minute Puzzle Book are both excellent and published by World Scientific.

The hole punch puzzles were written by Mark Chubb. There are sheets of these puzzles that you can download. Thanks to Mark Chubb and World Scientific.

There is a full reference to the paper mentioned above. There are effects of spatial training on mathematics performance. There is a journal about developmental psychology.

On Mondays, I set a puzzle here. I always look for great puzzles. Email me if you would like to suggest one.

I'm the author of several books of puzzles, most recently the Language Lovers Puzzle Book. I give school talks about math and puzzles. Please contact your school if you are interested.

I will be giving a puzzles workshop on April 21. You can sign up here.