## Introduction: Beelzebub's Square Puzzle

While in quarantine, I began following the exploits of magicians and problem solvers on YouTube. I witnessed the conquest of this puzzle originally by the one and only Chris Ramsay, a very talented illusionist, who is gifted in the art of solving puzzles. The object of this challenge is to create a solid square out of four identical pieces, whether you realize they're identical or not is also part of the challenge. What struck me about this puzzle in particular was that the concept, while simple in design, had an element of optical illusion. As an outside onlooker of mathematic principles and human optics, I would guess that this puzzle capitalizes on the use of irregular polygons and so spends minutes upon hours mocking our incapacities as self proclaimed omnipotent beings with thumbs. If there is any mathematician, psychologist, or exorcist out there who can explain the inner workings of this puzzle, PLEASE drop a comment!

If you're still in quarantine and want to mess with your fellow residents, you probably have paper, pen, and scissors at your disposal. If you're a nerd and have wood and tools, you'll definitely want to go the extra mile in these devilish activities.

Spoiler alert, even making this puzzle by hand does not guarantee that you will be able to solve it in one shot!

Credits to Chris Ramsay and his outstanding problem-solving skills. Believe me when I tell you I searched the internet high and low for the video of this puzzle to embed in my 'ible and came up empty handed. I guess we're dealing with a different kind of magic here.

## Supplies

Paper

Pen or pencil

Scissors

Saw

Wood

Sandpaper

Mineral oil

## Step 1: Just an Ordinary Piece of Paper... or Is It?

There is nothing special about the paper I'm using, other than the fact that it's a perfect square. I have the UConn School of Nursing to thank for that. This puzzle relies on near-perfect geometry in order for the illusion to work, so you'll need to find (or make) a square of any size. This one is a nice 3x3, which will yield a nice sized puzzle.

What we need to do with the paper is find the dead center. Start folding into perfect halves, both diagonally and horizontally across both axes. All creases will lead to one point: the center.

## Step 2: Prepare to Shift

This is where the magic happens. Mark a nice dark cross on the paper as shown above. As you'll see, this marks out four 90° angles. In order to make four puzzle pieces of the same size, the whole cross needs to be rotated. I figured that a 10° rotation would suffice. A protractor is handy, but I ended up free handing it pretty spot on using another piece of paper as a square edge. Extend all of the newly drawn lines to the edges of the paper. See where this is going yet?

## Step 3: Snip Snip Snip

Cut along your newly drawn lines. You will end up with four identical pieces. Freaky, huh? What's weirder is that there are TWO 90° angles in each piece! Your brain just doesn't want you to know that.

I took the time to check my work with my handy dandy protractor app. Right between 10 and 11 degrees!

To be honest, I feel that the amount you rotate would not truly matter. What really mattered to me was making sure that every single angle would be mostly unrecognizable. That's the key to the trick. I think 10° really helped me accomplish that, but try another angle for yourself if you'd like!

If you don't have wood, you can end here and try to reason out the puzzle with just the paper. Flip the pieces over so you won't be able to see the pencil marks. It's harder than it looks!

If you're advancing to a wooden puzzle, all you'll need is one of the four pieces. No need to choose wisely, they're all identical.

## Step 4: For My Next Trick, I Will Turn This Piece of Paper Into a Block of Wood

If you've opted to go the extra mile, go find a nice thick piece of wood. Take one of your puzzle pieces and use it as a stencil to mark out one piece. Run that through the saw of your choice.

## Step 5: One Piece Becomes Four

This was another aspect of the puzzle I had to consider. Sure, it would be easy enough to cut a perfect square out of a piece of wood and do the whole song and dance of marking your 10° angles from there, that way you can omit a whole slew of steps. Sure. BUT you'll actually end up ruining the geometric beauty of the puzzle if you do this. Your victim will end up worrying about splicing the grain instead of struggling through matching up the angles. I guess if you're merciful you can go this route.

If you love hindering people, go ahead and rip that piece of wood in half, then into halves again. You'll now have four identical pieces. Oooooooo ahhhhhhhh...

## Step 6: Check Your Work

What if I told you these pieces are all the same size? Try to see if you can solve your puzzle before refining it. As you can see, I had to make a few attempts before solving my own puzzle.

## Step 7: Final Touches

I used 180 and 320 grit to help refine the shape and smooth out some rough edges. I took a damp paper towel and used it as a tack cloth to help collect the extra magic dust. Lastly, I used mineral oil to bring out the color of the cherry wood.

## Step 8: One Last Thing...

Of course I had to try this puzzle again. Of course it took me multiple attempts. I don't wanna talk about it. I'm still omnipotent.

Thanks for reading! If you enjoyed this act, give a vote for the contest!

Participated in the

Toys and Games Challenge

## 13 Comments

3 years ago

One suggestion to eliminate the trial and error fitting (eliminating the center square hole when fitting together). Use a small square, or cut out an inside 90 degree angle and make a mark the same distance from the corner on each leg. Make the distance less than the side length of the wood square. The closer to the side length, the smaller the angle. For a 2” square, a leg length of 1 5/8” will give close to 10 degrees. Then draw a diagonal line on the wood square, line the angle inside corner on the diagonal line, and one leg mark on each side of the square with some rotation of the angle. Don’t make the legs parallel to the square sides. Draw along the legs, and cut on the lines. This makes the center fit tight when solved because these two cut edges are the ones that touch when solving the puzzle and they are the same length. Not the two on one piece, but one each of two pieces of the puzzle. Once you make one of these, just replicate 3 times for a total of 4 pieces.

Really like the instruct and the puzzle. Made for all the kids.

Reply 2 months ago

Do you mean 4 identical shapes like you showed, or 4 different sized shapes, with an offset "centre" of sorts ?

Reply 3 years ago

Thanks for this! Well above my level of math!

3 years ago on Step 8

very nice - easy to make and my young grandkids love it!

3 years ago

You lost me on the ‘turn one piece of wood into 4” step... Am I just using the same stencil 4 times? (To keep it challenging, making sure the grain is random) So just cut out one paper template, and use that one template to make 4 identical size/shape pieces? Thanks!

Best Answer 3 years ago

All Sam is saying... if you don't mind me jumping in.. is to use one stencil (they are all the same shape...) and give it depth, so a piece the thickness of a piece of paper becomes a piece of wood, maybe 1-2" thick. Once you have that, just slice it into pieces like a loaf of bread. This could be pretty sketchy with a bandsaw so be sure to clamp the piece well before cutting.

Reply 3 years ago

Seconding @sumitch. You have one piece at a pretty decent thickness. You rip that one piece into quarters, which gives you four identical pieces.

Reply 3 years ago

"In woodworking, a

rip-cut is a type of cut that severs or divides a piece ofwoodparallel to the grain."Answer 3 years ago

Using your 1 paper stencil, trace it out on a piece of wood 4 times, cut out each of the 4 pieces of wood and place them so that together they form a perfect square.

3 years ago

Place the 4 pieces of wood so they form a perfect square.

Reply 3 years ago

Thank you for clarifying! Looks like my edit wasn't added to the instruction yet...

Question 3 years ago

i've not really understood in what consist the magic of this puzzle....

i mean, i've my 4 pieces and.... what i've to do?

my spectator what have to do with my 4 pieces of square wood?

thank you

Answer 3 years ago

The magic is geometry and optical illusion

o.O O.o

It's really more of a riddle. Ask your participant to create a perfect square out of the four pieces. Works best if you shuffle them beforehand.