# Logic Puzzles, Part I

There are of course many natural links between the enjoyment of mathematics and the enjoyment of solving logic puzzles, but it’s not such a simple 1:1 correspondence. I’ve taught pupils in the past who project the “I hate maths” image with aplomb but whose eyes have lit up at the prospect of having a sudoku puzzle to solve. Equally, as a mathematician, I don’t see all logic puzzles as equal: sudoku in particular bore me beyond belief. [Note: MEI’s Core 4 paper always has a Section B exploring an interesting aspect of maths. In June 2008 it looked at latin squares and sudoku puzzles!]

Following a bit of Twitter chatter yesterday evening with @MissWillisMaths, @missradders (Hannah) and @RJS2212 (Robert Smith), I thought I would put together a couple of blog posts on the topic.

## Logic puzzles are good for you

I don’t know about research into brain-training and whether it helps us keep our marbles that big longer in life but, when I say logic puzzles are good for you, I mean they cultivate good working habits: digesting a formal set of instructions; sticking at a problem which initially may seem very difficult; identifying, forming and reusing strategies – those little ‘tricks’ that help crack the nut; and working within the constraints of a game of full information. All of these skills would be beneficial to a developing mathematician.

## Variety

My main beef with sudoku puzzles is their repetitiveness. There is relatively little logic to apply beyond “what numbers are missing here? what numbers could possibly go here?” and it’s not too difficult to write a computer program to solve at least the easier types. I enjoy the variations that are created as they bring a bit of novelty for a while: diagonal (or X) sudokus, jigsaw sudokus and so forth. This website describes many variants if you are interested in seeing them. I did once give a Year 10 top set a sudoku puzzle that used Chinese numerals – they loved it for its quirkiness and raced to solve it.

## More Variety

The other main reason I don’t solve sudoku puzzles is that there are so many other types of puzzle out there. They often have multiple names, typically including a Japanese name, but have you tried:

The list is all but endless. Bridges is top because I was addicted to that for a long time, and still really enjoy solving them (they make good use of the pigeon-hole principle)!

## Sourcing Puzzles

During our Tweets last night, we reflected that often the ‘cheap shops’ are a great place to pick up puzzle books. I bought one in Aldi yesterdy – £1.99 for 250 mixed puzzles – and years ago I picked up one in The Works – £2.99 for 350 puzzles. Just typing Japanese puzzles on Amazon brings up over 16000 results.

There is also a website/app I must point out as I think it’s amazing: Simon Tatham’s Portable Puzzle Collection. If you have never been to that site, then go there now! There are almost 40 types of puzzle that can be played online or downloaded and played – some are great on an interactive whiteboard, for example. You can also use the Windows programs to print sheets of puzzles of varying difficulty. Projecting an easier problem in the classroom is also a great way to introduce students to the rules.

The set of puzzles is also available as a free Android app and iPhone/iPad app.

Some tips from that collection: rectangles (great for thinking about factors); galaxies (tricky but includes rotational symmetry); and untangle (for D1 students to understand/see graph isomorphism).

## Some Novel Puzzles – Kropki and Sum Code

Last night I posted a couple of puzzles to Twitter as I had not come across them before.

The first was called Kropki (Polish for dots, and apparently also the name of a pencil and paper variant of Go):

I really like this one as there are no numbers written inside the puzzle grid to begin with. (Hint to get started: consider the bottom row and left column.) Futoshiki puzzles often have sparse or empty grids too.

The other puzzle I shared is one that I’ve used many times with pupils over the years. It involves some nice elements of arithmetic, with the limited pool of numbers from 1 to 26. The book it’s from calls it a Sum Code, but I’ve not seen them anywhere else.

In my next blog post, I’ll write a little more about how this puzzle could be scaffolded to best effect in the classroom. (Hint to get started solving it: clues 1 to 3 together give you C, then the rest of the clues are quite carefully ordered.) Edit: I’ve now written Logic Puzzles, Part II.

## Working Habits

I’ve found Notability a great way to work on all of these puzzles: I open a blank document, take a photo with the iPad’s camera and then work on the puzzle using Notability’s different pen tools and colours. It’s easy to undo mistakes and means I keep the original puzzles ‘clean’ and can photocopy them for a class.

Of course there’s also good old-fashioned pencil and paper, too!