Friday Puzzles #7

Place holder because I’m late and I’m heading off this weekend and bleh.

Another couple of double-toroidal sudoku coming…

adios!

Friday puzzles #6

Wow – I’m like totally on schedule. And I’m going to introduce double-toroidal sudoku. Basically it’s sudoku, which lives on a double-torus. Now, the inherent geometry on a double-torus is not Euclidean, but hyperbolic. All that means for those I’ve hopefully confused is that you can’t get a rows and columns arrangement placed on it – which is why this looks a little different. The puzzle is “octagonal” in shape – and just as you glue opposite sides of a square to get a torus, you can glue opposite sides of an octagon to get a double-torus.

So here’s what you need to solve it. There are 6 marked regions with which you want to place the numbers 1-8. There are also 8 “bands” – which start from the centre of each edge of the octagon, and work their way to the opposite edge of the octagon through cells which meet at opposite edges. These are 8 cells long, and again you want to place the numbers 1-8 in each. Basically, it’s exactly the same idea as Penrose sudoku

Finally, there are 2 bands around the perimeter of the octagon, each 16 cells long. (Can you see them?) Any consecutive 8 cells in these two bands again contain the digits 1-8. All of these constraints together are actually very strong – so a lot of the clues below are unnecessary. However I made the puzzle easier so that you can figure out some of the nuances of the puzzle’s geometry in time for a monster next week. :)

    #010 Double-Toroidal Sudoku – rated medium

All puzzles © Tom Collyer 2009

Friday puzzles #5

Back after a gap of too long I know, but here are two nurikabe puzzles. If you’ve forgotten the rules, I refer you back here.

    #008 Nurikabe – rated medium

    #009 Nurikabe – rated easy

All puzzles © Tom Collyer 2009

Friday puzzles #4

Following its incredible introduction to the world in the finals of the first sudoku world championships in 2006, the toroidal variant gets the pulse of any enthuasiast racing. My effort is in much the same spirit as that original.

The rules are: Fill in each column, row and each region with the numbers 1-9. Some of the regions run off (for example) the top edge of the grid. They continue up from the bottom edge of the grid. Similarly with the left/right edges. The idea is that if you take a nice square, glue left side to right side, and then the top edge – now a circle – to the bottom edge you get a torus – and hence the adjective toroidal. Although if you too are a dabbler in the dark arts of pedantry, you will have noticed that actually a classic sudoku is also “toroidal”. But arguably not as hard. :)

All that is left to be said is this puzzle deserves a slot by itself. Back to two (or more) next week!

    #007 toroidal sudoku – rated hard

All puzzles © Tom Collyer 2009

P.S. The next 2-3 Friday’s might suffer some delays too. I’d say there is approximately a 1/7 chance of the puzzles being published on a Friday, but I’ll nevertheless try to keep to the deadline!

Friday puzzles #3

Ok, so delayed a little later than Sunday. I’ve been busy.

On the other hand, here’s a sudoku with the givens in the shape of a Yin-Yang. Only I’ve just noticed that’s only true modulo a reflection – and we all know the sorts of trouble that quotienting out by an involution can get us into. So tomorrow I’ll put up a properly shaped puzzle. :)

Enjoy this incredibly easy fodder for now though!

    #005 sudoku – rated easy

EDIT: Here is the new, improved, properly shaped and rather nicely themed version, if I do say so myself. However, the large number of givens really does mean that it is still very easy.

    #006 sudoku – rated easy

All puzzles © Tom Collyer 2009