As you probably know, my online pseudonym is Puzzle Doctor (occasionally branching out to THE Puzzle Doctor depending on how self-important I’m feeling 🙂 ) but only part of the “Puzzle” bit relates to my reading preferences. It also relates to actual puzzles, which I’m also a fan of.

Last month I was very proud of two things – being able to help out at the World Sudoku Championships and competing for the United Kingdom in the World Puzzle Championship. I mentioned it in the Puzzly post and there were a couple of requests for more information. So here we go…

First of all, what are these Championships? Well, they are both run by the World Puzzle Federation – each country that is a member of the WPF can enter a team of four competitors. A different country hosts each year and arranges the specific format of the competition, with most of the puzzles set by people from that country. The competitors compete both as a team and also as individuals across two days – the team score consists of the total of the individual scores and the scores in some team rounds, designed for all four solvers to cooperate in finding the solution.

What sort of puzzles are involved here? Well, the sudoku competition is more than just normal 9 x 9 grids. The majority of puzzles will contain an extra rule – for example, no touching squares can contain consecutive numbers; no cells linked by a knight’s move can contain the same number, etc. If you would like to see the full range of puzzles, then follow this link to the UK Puzzle Association website – each puzzle type contains an example with the solution provided. I’m afraid for copyright purposes, I can’t link to the competition puzzles themselves, but this is the next best thing.

That’s the WSC, but what sort of puzzles are in the WPC? A much wider range that would take too long to itemise. The main condition on a puzzle being valid is that it is language neutral and does not depend on general knowledge. You may have seen examples in newspapers – Kakuro and Futoshiki make appearances in the UK press for example – but the variety extends far beyond that. Let’s give a couple of examples that you probably won’t have seen, copyright me (the puzzle itself, not the type).

**Japanese Sums** – in the grid, either shade the cells or place a digit from 1 to 6. The digits cannot repeat in a row or column, but all digits do not need to appear in each row or column. The clues for each row and column represent the sum of each string of digits (or single digit) in that row/column, which must be separated by at least one shaded cell.

**Tetronimos** – place the complete set of tetronimos (i.e. the seven Tetris pieces) in the grid so that the number by a row or column indicates the number of empty cells before the first used tetronimo is encountered. An unclued row or column means that there can be any number of empty cells, including none. The tetronimos cannot touch each other, not even diagonally.

This is only scratching the surface. Again, to get a feel for the entire range of puzzles that the solver is expected to deal with, this link will take you to the instruction booklet.

Well, I think I’ve said enough about the format. Come back tomorrow, and I’ll tell you something about what it’s like to compete in the tournament, and following that, I’ll direct you to some places to get loads of puzzles for free (mostly). And if you’re very good, I’ll post the solutions to these puzzles.

Hooray! I’m really excited to hear what it was like. My only experience was with the online application process about ten years ago, which I seem to remember just involved sitting in the lounge with a massive printout of puzzles and then running out of time.

I haven’t seen those two puzzle formats before. The second one looks daunting, although I guess similar to Battleships? Editor’s curse: surely it’s tetroMiNo, like domino? It’s hard to pronounce either way!

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Okay, so in wondering about the spelling of tetromino, I completely misread the rules! Wood for the trees. The clues indicate EMPTY spaces.

But with that in mind, I don’t see how there can be a unique solution. Before you even begin to fill in the grid, the clues show there’s going to be an isolated 3 x 2 space in the bottom left. Obviously the long piece can’t fit there, but surely whichever piece does eventually go there can be in one of two arrangements? Or am I being dense?

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Oh I am!

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The solution is unique. Stick with it…

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With my stupidity cleared up, I have a question: is it considered cheating to use the fact that the puzzle has to have a unique solution to skip steps? I seem to recall a term like “meta-solving” or something like that, and it being frowned upon.

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It’s not ideal but it’s a valid method. A puzzle SHOULD havea logical solution path that doesn’t require using the uniqueness but not sure people actually frown upon it. In fact for some puzzles – No Four In A Row and ABC-Connection, it’s used quite a bit.

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Hmm. Now I wonder if it’s possible to construct a puzzle where the ONLY way to solve it is to rely on the uniqueness of the solution (and the solution is indeed unique). My intuition is that it wouldn’t be, but I also have a niggling feeling that might be deep into Godel territory, and it’s the sort of weird thing where you can prove it’s possible, but never demonstrate an example (I studied mathematical philosophy at uni, but I found my first Henry Merrivale books during the week we did the Incompleteness Theroems and I didn’t pay much attention!)

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Not sure about the only method, although the Arukone/ABC Connection puzzle is usually solved much more quickly using the uniqueness property of the solution.

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In sudoku also, the uniqueness method often provides a breakthrough. I have also found that in very difficult sudokus, intelligent trial and error is a faster method than the standard logical methods like XY-wing, XYZ-wing, Swordfish etc where discovering the pattern itself is time consuming. After all, time is of the essence in championships.

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[…] learn what the actual experience of the competition is like, but in the meantime the Doc has put up two puzzles of the kind you’d see at the championships, although these are his own creation. The first is Japanese Sums, the second is Tetrominoes. Do […]

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If anyone wants the solutions – with excellent explanations, btw – do pop over to richmd’s blog where he’s written a step-by-step solving guide. Thanks, Rich!

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Well beyond my pay grade guys, to put it politely (“I’m a lawyer, not a mathematician, Jim” – fascinating all the same and my sister-in-law would be all over this 🙂

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Well, I am a mathematician or a least got an undergrad degree in Mathematics many many years ago, but still way beyond me. I used to love logic problems but even those began to be too much for me years ago. But I loved all this info. And eager for more.

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I found the post quite interesting. I am also very keen on Mathematical Puzzles. I have a large collection of books on Mathematical Recreations including the entire Martin Gardener set.

I do not regard the uniqueness method as cheating. I often use it to solve sudokus.

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[…] ← The World Puzzle Championships 2014 – Part One […]

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