*No Tens Sudoku*

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## June 04, 2010

### Friday Puzzles #55

Mission accomplished! Weekly numbering is now completely in order. Modulo the missing #7 and #17 that is. Still, there were a couple of weeks where I made bonus puzzles so I think that just about balances out the equation. I must add that I revisited the double-toroidal sudoku, but I have to say that with its current grid I lost a bit of interest.

Anyhow, a sudoku variant this week which I think I’m right in claiming has only ever been pulled off by yours truly – although please correct me if I’m wrong. In case you missed the original post the idea with 10’s sudoku is normal sudoku rules, except that every time a pair of adjacent cells had digits summing to 10, they are marked. Where there are no markings between adjacent cells, the conclusion is then that the relevant digits cannot sum to 10.

Prior to that post, I can’t find an example where 10’s sudoku had no such marked occurrences between pairs of digits, but it turns out with a bit of work that it’s perfectly possible. I’m sure a computer-y type would easily be able to write a program to churn out more of these without working up any sort of a sweat, but that’s not the way I roll. There’s plenty of potential with this variant to churn out some really fiendish challenges; this example is fairly plain sailing, but perhaps with a couple of surprises along the way. Enjoy!

**UPDATE:** My apologies to those who had a go at an earlier version of this puzzle, which had two solutions, and my thanks to Jack who pointed this apparently obvious blooper I managed to completely miss! My reputation for errors seems to be growing, but stick with me anyway – at the very least you won’t be bored!

All puzzles © Tom Collyer 2009-10

## August 14, 2009

### Friday Puzzles #10

This week comes with a bit of a special theme. The number 10. It’s also very special in that I have managed to get this out and published on a Friday. Wow!

As regular readers may or may not know, last April I participated in the 4th World Sudoku Championships, hosted in a dusty provincial Slovakian town called Zilina. Much was made of the (lack of) quality of many of the puzzles – but one of the most enjoyable puzzles was a variant that appeared in the semi final:

Puzzle M3– World Sudoku Championship, Zilina 2009

The idea was simple – take a classic sudoku, and mark exactly where an adjacent pair of digits summed to 10. So if a 3 and a 7 were next to each other, a cage was drawn round and marked 10. The twist with this is the contrapositive inference – that is if no cage exists round a pair of adjacent cells, *then the numbers inside cannot sum to 10!* The puzzle itself had only one such pair of numbers marked – which made me wonder if actually you could go one better and perfect the puzzle.

Well, it turns out you can. After a lot of painstaking work to first even find a valid solution grid, I then wrestled with the task of making a decent puzzle – with my given visual theme. The result isn’t particularly challenging – though not totally trivial.

I do also have a couple of very hard puzzles too. They turned out to be hard almost by chance – they certainly aren’t a particularly pleasant solve in my opinion and so I haven’t bothered publishing them. Anyhow – without further ado, here’s the preamble: place the digits 1-9 in each row column and marked 3×3 box. Digits in adjacent cells may not sum to 10.

#014 No Tens Sudoku– ratedeasy

All puzzles © Tom Collyer 2009. Well, obviously excepting the world championship puzzle above. I have no idea who to credit that to – and whilst used without permission, I’d like to think that demonstrating it would come under fair use. Anyhow, please respect the rights of the author.