Is This Curve Infinite?

Hilbert from Abhishek Ruikar
This version in Oak

Out of the blue, a couple of months ago, I was contacted by Abhishek informing me of his latest creation and asking whether I wanted one. I had just mortgaged my soul to the devils (aka Dee Dixon and Tye Stahly) and asked whether he would wait a month for me to replenish my PayPal and also soothe over the disgruntled first wife (Whack! Ouch!)

He was very happy to wait for a bit and duly reminded me after a suitable period. Luckily, I had a little spare cash and it flew over the wires to India. This puzzle is available in Oak, Ash, Teak and Mahogany - I decided on the Oak version but they all look nice.

It drives in a nice green box (the corners of mine had taken a slight beating from the postal service) and inside is a little folded leaflet with the instructions (and if you need it, the solution).

Abhishek obviously has a penchant for knots and topology as his previous puzzle also involved wooden pieces with magnets that needed to be assembled into an intertwined shape. I needed to resort to Google to understand the name of the puzzle. I was aware of David Hilbert as a famous mathematician but did not know why this puzzle was named after him. Within a minute the reason sang out to me - the Hilbert curve is a fascinating concept describing fractal curves that can be both 2D and 3D space filling:

Hilbert curve courtesy of Tim Sauder

3D filling by Robert Dickau

When I removed the pieces, I realised that there were 8 of them and they all have similar but not identical shapes and now the reason for the name really became clear. This is a 3D filling puzzle:

8 very similar shapes with magnets!

I set to work making chains of pieces to try and form a cube. It didn't look too tough and was helped by the fact that the polarities of the magnets were the same on the equivalent ends of all the pieces. After about a ½ hour, I realised this was not quite as simple as expected. The pieces fit together making interesting shapes but after 5 or 6 of them the curve interested itself or blocked the insertion of the next piece. I made several dozen interesting shapes that didn't go anywhere:

Not getting anywhere!

Finally, I got fed up of random assembling of pieces and actually looked properly at the shapes that I had - there are 4 pairs of identical pieces which need to be arranged into the cube shape. It could not possibly be a random assembly - they had to work in a logical sequence which needed me to to some think©ing.

4 pairs of pieces

Once I understood this, then there was much less random trial and error. Thinking in terms of 6 faces and dividing up 8 pieces as 4 pairs was not helping me at all. It needed a few attempts at looking how the pairs could be arranged and thinking of edges (there are 8 in a cube) and I had a lovely little Aha! moment and managed to arrange my magnets in such a way that they all met end to end and formed a cube. Simply delightful - combining mathematics and mechanical puzzling cannot be beaten!

A Hilbert cube

Thank you, Abhishek, this was a delight. I have just realised that putting the pieces back in the box will be another challenge!

 I am sure that he would be delighted to sell you a copy if you contact him.

A Knot Without String

Knot by Abhishek Ruikar

Abhishek has burst onto the puzzle scene from nowhere and seems to have produced a few very well received puzzles over the last year or so and I had missed them all. He showed off the Knot a couple of months ago on the Mechanical puzzle Facebook group and I couldn’t resist it. It was made of wood and had an interesting idea to it. When Neil reviewed it on FB and was pleased with the idea and puzzling level, my decision to buy was confirmed. Contacting Abhishek directly through FB messenger was a breeze and I purchased directly from him using PayPal. His designs are now available from PuzzleMaster as well as Nothing Yet Designs and I can recommend them.

It took a while to arrive from India because Abhishek was away from home when I contacted him and the British postal service seems to be falling to bits these days. I was delighted when I opened the box because the presentation was unexpectedly beautiful. There’s a nice black box with the name printed on it which slides open to reveal the Teak puzzle pieces held in foam and an instruction card alongside. It’s as if it’s been made by a professional puzzle supplier. 

2 sets of chiral tetrominoes
Magnets in seemingly random positions

The Teak is well finished and the magnets flush with the surface. I was impressed. A quick inspection revealed that the magnets seemed to be randomly positioned and with odd polarity. Each piece was different. The name and the instructions say to assemble into a complete trefoil knot with everything held stable by the magnets whilst none of them are visible externally. Easier said than done for a puzzler who is terrible at assembly - destruction seems to be my forté.

Initially, as I do with most puzzles, I start with randomly trying things. Luckily, there’s a diagram showing the aimed for shape and I place pieces in a way to achieve that only to find that the magnets won’t match with each other or actively repel. At one point I did seem to be making progress but the last couple of pieces couldn’t fit together without one of the magnets being visible externally. Whilst this was actually quite a pleasing thing to achieve (at least I had the shape correct) but not having all the magnets connect meant that it was not stable. If I let go of any piece the puzzle was going to fall apart.

After about ½ hour of almost getting there, I realised that I had to be a bit more analytical. With 6 pieces, I could not keep track of what I had tried in which position and had to actually think a bit about directions and polarities. Once along this path, I made pretty rapid progress and had my solution in another 5 minutes. The Aha! moment was delicious and a photo was taken shortly afterwards.

Aha! A nice Knot

How should I store it? The box is so good that I have dismantled it and will be keeping it in the box for display. Interestingly, repeating the solve had to be done from scratch - there seems to be no way for me to remember the assembly. Don’t tell Mrs S that I could just solve this over and over again with no recollection of previous solutions.

This is well worth the $75 from NothingYetDesigns if you like a nice little assembly challenge. It is not yet available from PuzzleMaster.

Thank you Abhishek for the fun puzzling. I will look forward to the next creation from you.