The first puzzle is a super-fun 25×25 nonogram puzzle
Before Christmas, the benign megasurveillance bods at GCHQ released a set of festive puzzles, in the form of a Christmas card and associated website. An initial nonogram puzzle led to a sequence of increasingly fiendish teasers, and solvers of the final set of puzzles were invited to email in their answers, with the correctest winning a fancy paperweight, signed book and, GCHQ were at pains to stress, not an Imitation-Game-style secret job offer.
If you were wondering what happened with all the left-over wrapping paper from this morning’s post about wallpaper groups, Katie has made a YouTube video demonstrating some mathematical quirks of gift wrapping. Enjoy!
Christmas wrapping paper is sold in thousands of different variations, including plain, coloured, patterned, foiled and even flock, but one thing it’ll have in common is that it will repeat whatever pattern it has, regularly across the design.
I’m interested in symmetry, and was intrigued to find a curious fact about the symmetries of such repeating patterns – their symmetries are quite limited.
It works by mapping a triangular design onto a blown-out icosahedron, and applying some “kaleidoscope effects”. As far as I can tell, that means they expand and rotate the patterns so they overlap.
There’s a selection of built-in patterns you can choose from, or you can upload your own pattern to make a really unique decoration. However, because the resulting object needs to exist in the real world, you need to take care to make sure it all comes out in one connected piece. Shapeways have written some very clear instructions about how to achieve that.
As part of Puzzlebomb’s commitment to bringing you all puzzles, all the time, we present a special one-off edition, consisting of festive wordplay. Enjoy! Solutions will be posted in roughly a month from now.