A short “2016 UK Puzzle Championship” season begins with a piece about how to get started with the puzzles in the competition. The piece needs context, however; participants have frequently commented that there weren’t many easy puzzles in the contest, yet participants’ scores tended to skew relatively high, compared to previous years’ contests. It’s also worth pointing out that I tend to come near the bottom of the rankings table, typically beating about 20% or so of the other competitors. Accordingly, take what I say with a considerable pinch of salt – but, on the other hand, there aren’t many people talking about the puzzles. Considerable credit goes to James McGowan for posting links to practice puzzles in advance.

You are strongly recommended to download the puzzles, open them using the password ` 20_S3n3c_16` and look at them in parallel with this commentary. First and foremost, thanks to the puzzle authors for their contributions and to Liane, Alan and David for putting the contest together and making sure that it happened at all. I thoroughly enjoyed the event.

**1. Bank Note** Theoretically puzzle 1 is something that can be done quickly while you wait for all the rest of the puzzles to print out. I found this year’s tough for a puzzle 1, taking completely the wrong approach at the start. Treat the horizontal and vertical numbers separately, and write each row or column number as the sum of numbers from 1 to 5, such that each number appears once in one direction and in three adjacent rows or columns in the other direction. So the 1 means there can’t be anything in that row but a 1, so if there are vertical numbers then they must span the top three rows, which gives you a clue as to where the 5, 3 and 2 are.

**2-3. Last Digit** I solved puzzle 2 and entered it with less than ten seconds to go, which *definitely* beats finishing a puzzle just too late. Count up which gaps have 2 numbers pointing to them and which have 3 pointing to them. You can’t have a sum of three numbers from 1 to 7 being over 20, so the sum must be between 11 and 17. These puzzles were not popular with UK solvers.

**4. Skeleton Crossword** Word puzzles used to be easy but laborious, but these days they’ve got rather harder. I don’t see the breaking-in point here.

**5-6. Paint it Black Railway** You can extend the line in each direction one square from each of the crossover points, and thus determine the directions in which the line passes through stations 1, 4 and 6. The presence of a line in the square above the upper crossover point means that there are only three possibilities for row 5, and the fact that each column has only one black square cuts down on the possibilities for row 4. On the other hand, I used similar logic on puzzle 6 and kept running into contradictions, or at least chunks of the map where the line has to enter and exit through the same square, which is clearly wrong.

**7-8. Magnets** After muffing my first attempt at Bank Note, I tried puzzle 7 as my second attempt and ran into a contradiction fairly quickly here too. The starting-points are rows with particularly many or particularly few magnetic tiles; fill these in as either magnetic or non-magnetic first until you become clear what the polarity must be. You can practice the genre in the Simon Tatham puzzle pack, though solving it on paper differs more from solving it digitally than you’d think. I got puzzle 7 correct on my second attempt and didn’t touch puzzle 8.

**9-10. Arrows** I don’t see the breaking-in point and this genre did not prove popular with UK solvers. Plenty of examples are available for practice.

**11. Star Battle** An unusually large example of the genre that did not prove popular with UK solvers. It’s easy to identify lots of spaces where stars cannot be, but I couldn’t get far enough to actually place many stars. Plenty of examples are available for practice.

**12. Battle Stars** The starting-point would seem to be rows and columns with few possibilities, but I couldn’t break in to this one. Some examples have been published.

**13-14. Clouds** The zero column offers a start, and it’s easier to think in terms of rows and columns featuring 8 filled squares being all filled *except* for two squares which separate clouds through the “don’t touch each other, even diagonally” rule – and the “must be at least two in each dimension” rule cuts down the possibilities, so an 8 must be a 4-2-2 or a 3-3-2 in some order. Plenty of examples are available for practice.

**15. Tapa** Another fairly well-known puzzle style, but not one at which I am much good; I spent a few minutes and couldn’t get far at all. Plenty of examples are available for practice.

**16. Dissected Tapa** Tapa has spawned plenty of variants, probably not very many fewer than there are sudoku variants. I am told examples of these cropped up in this contest and contest 18 in the same series. I didn’t touch this.

**17-18. Sum Skyscrapers** Start by working out where the 5s must be. A 9 column could arise from a 4-5 or a 1-3-5, a 12 could be a 3-4-5 or a 1-2-4-5… and what the consequences would be when looking at the column from the “other end”, when you have values for both ends of a column. This is a variant of a well-known puzzle type in the Simon Tatham puzzle pack.

**19. Hidoku** This was the first puzzle I properly solved, after muffing a few attempts. Start in the lower left corner and work out which numbers you have no alternative but to place. This will all but fill in the lower left square, with a few strings of gaps. There are 104 squares to fill, so you can fill some of the gaps with 102 to 104 (for where else can they go?) and then 1 to 5. By this point you can work out what the numbers are in the squares between the big squares and then just treat it sas four smaller examples. Plenty of examples are available for practice and I think they’re in newspapers as well. The most frequently correctly solved puzzle on the paper.

**20. Kakuro** A large example but no particularly nasty tricks, though I think the bottom appeared to have two possible solutions, one of which could be ruled out fairly quickly because it broke the bottom right. The way to break into this is to break it into more manageable chunks and draw what conclusions you can, especially from sequences of particularly high or particularly low numbers – a 17 over two digits must be a 9 and an 8 in some order, a 16 over two digits must be a 9 and a 7 in some order, and so on. Again, plenty of examples are available for practice and I think they’re in newspapers as well.

**21. Sum Snake** A variant of the Snake format. An example was featured in another contest. I didn’t touch this.

**22. Pearl Areas** No clue.

**23. Filled Pentominos** Didn’t touch this either.

**24. Sumpix** I did solve this and was delighted to do so. The technique is to look at sums of adjacent numbers. As the lowest sum of four adjacent numbers is 1+2+3+4=10, the lowest sums of three adjacent numbers are 1+2+3=6 and 2+3+4=9, the sums of two adjacent numbers are either 3+4=7 or 4+5=9, you can conclude that the 8 column is an 8 only. From there, next look at the columns with totals near 55; the 50 column is missing 5 and thus could be missing 1+4 (i.e. 2+3+5+…+10), 2+3 (i.e., 1+4+…+10) or 5 (i.e., 1+…+4+6+…+10), and similar logic for the 51 and 52 columns, which means that you can mark in at least the 6s-to-10s in those columns. Next, look at the 39 and 40 rows, bearing in mind the 8 column. That’ll get you started.

**25. Killer Sudoku** Standard, though a 40-point example looked like it had the potential to be quite mean. You don’t need me to provide a link here.

**26. Hashi** Standard but large and very easy to make a mistake on at this size. You can practice the genre in the Simon Tatham puzzle pack, though solving it on paper differs more from solving it digitally than you’d think.

**27. Suguru** Another popular example of a style that I’ve never really got into as it’s so possible for a single mistake to ripple through and affect lots of other cells before you spot the error. Plenty of examples are available for practice.

**28. Slitherlink** Slight variant of a familiar style. You can practice the genre in the Simon Tatham puzzle pack.

**29. Sum Fillomino** Variant of a familiar style. You can practice the genre in the Simon Tatham puzzle pack (“Filling”) though I don’t know how to use the constraints of the variant to break in here.

Tell me when I make no sense anywhere below.

Battle Star in 5 steps:

https://drive.google.com/open?id=0B5dfTk5mjCGHdjJITWtqRlprUkE

Star Battle in 8 steps, in one picture.

https://drive.google.com/open?id=0B5dfTk5mjCGHYmR6R3hTNmI4WWs

The former was a whole lot easier 15 points.

Arrows are mostly about accounting. You need to mark directions your arrows can no longer point towards, and add a tally mark to every cell a newly placed arrow points at. The usual start is when cells with high and low values are aligned. Note that high means close to 8 in general, but close to 6 on the diagonal and close to 4 in the centre. In puzzle 9 for example, we start with the 6 which has 1s both horizontally and vertically. Each 1 removes a potential arrow from the maximum of 8, so we need all the diagonals to point to 6, and also none of the diagonals to point to these 1s (as well as their other orthogonal direction).

I’d welcome some clouds/radar instruction actually; I suffer through them.

The hidoku was truly lovely.

Hated Hashiwokakero’s presentation: Gray lines in a puzzle where you draw with a pencil and have to distinguish between 0,1 and 2 lines at a glance? Also little whitespace between circles makes for tiresome connectivity checks.

One can get a whole lot better at Slitherlink in just two steps:

1) Learn rather than discover over time the given patterns. From http://puzzleparasite.blogspot.gr/2011/11/slitherlink-pattern-guide_23.html Not fun, but effective.

2) Realise that any closed line you care to draw will intersect a Slitherlink solution an even number of times. If you can’t be bothered to train a keen eye, painting the inside and outside of the Slitherlink different colours will make some of the applications of this special case of the Jordan theorem pop.

Just a quick note to thank you for your diagrams; very instructive! I’m OK at easy Star Battle on Croco-Puzzle but pretty horrible at them in the real world – another case of solving online behind different to solving on paper.

There’s a Hidoku in the 2011 UKPC. I managed to solve this 2011 Hidoku at the time, but can’t see how I would break into it now! Perhaps the route would be working out which legs of the journey might possibly fill in the corners?

First thing I check in a Hidoku is the slack between consecutive givens, that is how much their difference is over the length of the minimum reasonable path that connects them. In this one, 1-5, 17-21 and 21-26 are tight (difference of 0). Tight paths need to move to a closer column, or row or both on every step, so they are very constrained. 1-5 rubs against most givens, so I focus on that. Taking the path to the left (4@R2C4) creates a top right space where you need to draw ~5 lines (clues have a before and after line segment) out of just ~2 holes (R1C4, R5C7). That’s clearly not going to work, so 4@R2C6.

It’s now time to use the kind of thinking you were talking about, namely “How on earth can I reach the cells between 4 and the corner?” Turns out only 5-11 and 46-49 have reach. They can’t both go there, and 46+ isn’t long enough to cover everything, so 5-11 it is. This fills the top right, forcing 22,24,25, from tight 21-26, to go full left. This crowds 46, which needs to connect to R2C4 in one direction and R5C7 in the other. And from there on it’s mostly leaving no holes behind.

It’s also worth noting that abusing the promise of a unique solution can be very helpful in these problems. Numerous path shapes, some just a couple of cells long, have alternative routes using the same cells. Avoiding forming them can often radically simplify a problem. For example, needing to go from A to A+3 through B and C tells you you’re doing something wrong.

A

B C

A+3

Surprisingly (well, maybe) Battle Star was one of the ones I did. As xrm’s guide explains, rows 5 and 6 are your entry point.

It’s your comments on 26 and 27 that sum up my feelings towards many of the puzzles. I can find an entry point, but very quickly I come to a point where I’ve got (at least) two alternatives. So I say okay let’s try option A and follow it through. But even if that doesn’t throw up several alternative routes of its own, it still takes a lot of time and effort to push it through to a stage where you know its wrong, before going all the way back to option B. I know that isn’t what other people are doing, so I reason there must be a way of eliminating those alternatives without going down them, which I can’t see, so give up. Indeed 26 was the biggest one for this in the contest for me.

Ho hum, maybe next time.

Thanks for the write up (and for the original encouragement to play!). I really enjoyed taking part, even if I had a remarkably poor result. I’ll definitely try to carve out some uninterrupted time next year and maybe even look at the practice papers in advance (although there’s a certain satisfaction in taking on puzzle types that you’ve never seen before).

Also thanks to Mark for making me feel this wasn’t just the domain of puzzle gurus, but us “amateurs” could take part too!