Carnival of Mathematics 133

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Welcome to the 133rd Carnival of Mathematics, the monthly round up of maths blogs organised by The Aperiodical. Next month’s Carnival will be hosted by Comfortably Numbered. You can submit items for next month here.

133 is an octagonal number

133 is an octagonal number

Before we get going with the blog posts here are a few facts about the number 133:
  • The sum of the digits of 133 is 7, which is a factor of 133. This makes 133 a Harshad number.
  • 133 is an octagonal number.
  • Start with the integers; cross out all the even numbers. The second remaining number is 3, so cross out every third number. The next remaining number is 7, so cross out every seventh number. After completing this process, 133 will remain, making it a lucky number.
  • The symbols $\times$ and $=$ can be inserted into 133 to make a true statement ($1\times3=3$). 133 is therefore a didactic number.
  • 133 will be the number of the issue of Chalkdust Magazine which will be released in Spring 2081. For now, you’ll have to make do with issue 03.

There have been many excellent submissions for this month’s Carnival, so let’s get on with it!

Back in January, KPMG estimated that the National Lottery had a expected value greater than the cost of a ticket. This led Zoe Griffiths to buy her second ever lottery ticket. She did not actually make any money: her blog post explains why the expected value does not tell the whole story.

Four low order dragon curves

Four low order dragon curves.

It’s been a good month for pretty pictures of fractals: I had a play with dragon curves and Antonio Sánchez Chinchón went bananas with Hilbert’s curves. Both these curves are space filling, as they can completely cover a plane. They also both make excellent desktop backgrounds.

In March, Andrew Hacker’s new book, The Math Myth: And Other STEM Delusions, was released. Instead of attacking his views on the unimportance of maths, Ilona Vashchyshyn instead wrote about what Hacker got right. She emphasised the importance of answering his question: why is it important to learn maths?

The addition of coding to the curriculum has also recently come under fire. This rebuttal by 15-year-old Oliver Dunk gives a good number of reasons why coding is in fact a very important skill to learn. If you enjoy his writing, then keep an eye on our blog next week!

Over Christmas, many of you may have attempted the GCHQ Christmas puzzles. If you did, you will first have solved a puzzle known by different people as a nonogram, hanjie, picross or griddler. To help with this puzzle, Isaac Lee has written a blog post about solving nonograms with compressive sensing. Their code does not solve the puzzles exactly but may be good enough for the GCHQ puzzle, as it’s solution is a QR code and QR codes still work when they contain small errors.

If you prefer to solve your puzzles by hand, here are a few to go away and think about:

High-Stakes Cribbage

This puzzle was inspired by Brendan Sullivan’s Puzzle of the Week blog.

Adam and Brendan are playing high-stakes cribbage. They both start with an amount of money. The player who loses each game must double the other player’s money. (For example, if Adam (with £10) lost to Brendan (with £6), then Adam would pay out £6 to double Brendan’s money to £12, leaving Adam with just £4.)

If the player with the least money wins each game, then there are two possible outcomes: The sequence of games may end with one player having all the money; or, the sequence of games may continue forever?

What starting amounts of money lead to these two situations? 


This puzzle appeared in issue 03 of Chalkdust.
routesYou start at A and are allowed to move either to the right or upwards.

How many different routes are there to get from A to B?


This puzzle recently appeared on Futility Closet.
AB and CD are consecutive ties across a pair of railroad tracks that appear to meet at O on the horizon, H. If the ties are parallel to the horizon and are equally spaced along the tracks, how can we draw the next tie in this perspective figure? 

And if these puzzles are too easy, why not try our prize crossnumber. It should keep you busy until next month’s Carnival!

Next month’s Carnival of Mathematics will be hosted by Comfortably Numbered. You can submit items for next month here.

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Matthew Scroggs is a PhD student at UCL working on finite and boundary element methods. His website,, is full of maths and now features a video of him completing a level of Pac-Man optimally.
Twitter  @mscroggs    Website    + More articles by Matthew

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