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My adventures in 3D printing: Seven Triples puzzle

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

There are seven kinds of shape. There are three copies of each shape. The pieces like to group together in threes.

Can you arrange the pieces into seven groups of three so that for each possible pair of shapes, there is one group containing that pair?

Try to do it without paying attention to colours first, then try to rearrange the pieces so each group has a piece of each colour in it.

Small Sets of Arc-Sided Tiles

Tim has previously written guest posts here about tiling by tricurves, and is now looking at ways of tiling with other shapes.

In an earlier post elsewhere I covered some basic arc-sided shapes that tile by themselves. Lately I’ve been playing with groups of curved tiling shapes, asking a question common for me: how to get the most play value as an open-ended puzzle? This means getting the most interesting possibilities from the simplest set. “Interesting” includes variety, complexity, challenge and aesthetic appeal. “Simplest” covers not only size of set and the shapes, but also the least total information needed to describe or construct the shapes.

Making Tricurves

Tim Lexen has written a series of posts on the topic of Tricurves: Bending the Law of Sines, Combining Tricurves and Phantom Tiling. In this latest post, Tim has been working with our own Katie Steckles to turn Tricurves into real objects to play with.

When you discover an interesting mathematical shape or object, there’s a strong instinct to play with it – maybe by drawing sketches and doodles to test the limits of the idea. But in the case of Tricurves, drawing an accurate shape takes a little time, and it doesn’t lend itself well to idle experimentation.

Producing a physical version of a shape, in enough quantity to allow for experimentation, makes it much more tangible. In our own respective locations, we’ve each made use of laser cutting facilities to produce wooden Tricurve tiles to play with, and we encourage you to join in.

“Transposition”, a sliding block puzzle by Jacob Siehler

Start and finished states of a Transposition puzzle

This is just a quick post to tell you about a nice puzzle game I spotted on Mathstodon.

It’s called Transposition, and it’s a sliding block puzzle in the vein of the popular game Rush Hour. You’re given a grid that’s almost full of rectangular blocks, and you have to slide them around each other until the two coloured blocks have swapped places.

The puzzle was invented by mathematician Jacob Siehler, who says he used a computer search to generate a pool of puzzles, given the rules of the game. I took quite a while to solve all 5 “easy” puzzles – as with any logic puzzle, you need to play about for a while to get a feel for the mechanics. I hadn’t appreciated at first that the grey blocks don’t need to be in their starting places when you solve the board – only the coloured blocks need to in the right positions.

There are 26 puzzles at the moment, ranging from “easy” to “very hard”. Have a crack at it! I really enjoyed it.

Play: Transposition, by Jacob Siehler

Finding an equation that has the same solution when rotated

(x+8)/6=9/(5+x) or, flipped, (x+5)/6=9/(8+x)
Solve this equation for x. Then rotate 180 and solve for x again.

I made this. Here’s how…

A puzzle for another day

A few months ago, my faculty’s PR person sent an email round asking if anyone would like to write a puzzle for the Today programme’s “Puzzle for Today” slot, to be broadcast during the programme’s trip to Newcastle in Freshers’ Week. A colleague said this might be the kind of thing I’d like to do, which it was, so I started thinking, and eventually came up with a brand new puzzle which I thought would work well.

If you listened to the Today programme this Thursday morning, you’ll have heard not my name, but that of Dr Steve Humble, who’s got a lot more experience doing this kind of thing. Turns out, they wanted something more ‘visual and interactive’, so asked him instead. I think that was a polite way of saying they just didn’t like my puzzle. Oh well!

Steve chose a classic puzzle that coincidentally appeared on Twitter about a month ago, prompting much discussion. It’s a good puzzle, much better than the one I came up with, but I don’t think Steve was completely right to say “It is possible that you can always create a winning game” – that’s only the case if there are an even number of coins, but his statement said “around ten coins”. I suppose he might’ve meant that, starting from having a handful of coins, you can decide to only use an even number of them.

The upside is that I can now talk about the puzzle here, where someone might actually enjoy it.

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