# Killer Sudoku Variants

## Toroidal Killer Sudoku Pro

Toroidal Killer Sudoku Pro puzzle

Here’s something that I’ve actually never seen before – Killer Sudoku with toroidal cages.  Perhaps there’s a good reason for that, but it’s time to find out.    This is actually a Killer Sudoku Pro, so it doesn’t just involve addition – but you cannot repeat a number in a cage, unlike in CalcuDoku.

So the rules are:

• Place 1 to 9 into each row, column and bold-lined 3×3 box
• Place numbers in each cage to add/multiply/subtract/divide up to the total at the top-left of each cage
• Numbers may not repeat in a cage
• Some cages wrap around the edges of the puzzles, continuing directly opposite

This is rated ‘gentle’, and none of the toroidal cages are very large so shouldn’t be too confusing to follow (I hope!).

Good luck!

## Consecutive Samurai CalcuDoku

Consecutive Samurai CalcuDoku puzzle

Now this is an interesting puzzle!  At first glance it looks like it can’t possibly have a unique solution, since there are no givens and only 9 cages on the entire 3-grid Samurai puzzle (made up of 6×6 grids).  But in fact it uses only simple logic to solve, and it unravels pretty quickly once you get going.  It’s a pretty powerful demonstration of how much you can strip a puzzle back and still keep it entirely reasonable in terms of difficulty.  In fact it’s arguably too easy…

The rules are what you’d expect if you’ve been following previous puzzles, but in summary you must: (deep breath!)

• Place 1 to 6 into each row and column of the three underlying 6×6 grids
• Place numbers into each of the bold-lined cages so that they add up to the number at the top-left (or in the case of the 40x cage, multiply up to that value)
• Wherever a white bar divides two squares, the numbers in those two squares must be consecutive (so they must be one of these pairs: 1&2, 2&3, 3&4, 4&5 or 5&6)
• Where no white bar divides two squares, the numbers are non-consecutive

Good luck!

## Samurai 5-grid Killer CalcuDoku puzzle

Samurai 5-grid Killer Calcudoku puzzle

Here’s an interesting puzzle.  It’s a 5-grid Samurai Killer CalcuDoku, which means that it has the 3×3 boxes from Killer Sudoku but otherwise works like a CalcuDoku puzzle, albeit a 5-grid Samurai one!  All of the operations in this puzzle are addition, so aren’t shown.

Can you place 1 to 9 into each row, column and 3×3 box of each of the underlying 9×9 Sudoku grids, whilst also placing numbers so that each inner cage adds up to the total given at its top-left corner?  Numbers can be repeated within these cages (pretty obviously, given how large some of them are!).

There are quite a lot of single digit cells, suggesting (truthfully) that this isn’t actually a very difficult puzzle – but it’s a good proof of concept, I think.  You can create really huge cages if you want, without making the puzzle difficult (of course, the easiest way to solve these is to essentially ignore the cage completely, or at least until it is nearly finished).  This particular puzzle does not require you to do any complex maths at all.

Good luck!

## As Easy as 11, 22, 33… a Killer CalcuDoku

As easy as 11, 22, 33 Killer CalcuDoku

Here’s a relaxing puzzle for a Sunday… or maybe not!  Can you complete this Killer CalcuDoku puzzle made up of 1s, 2s and 3s?

Place 11, 12, 13, 21, 22, 23, 31, 32 or 33 into each square so that the result of applying the specified operation to each cage is the given number.  (Start with the highest number in the cage for subtraction and division cages).  Also, can you obey the standard Sudoku constraints: place each of the 9 different numbers once per row, column and bold-lined 3×3 box?  You can repeat numbers within a cage, however, if you wish (which is why it’s a Killer CalcuDoku, not a Killer Sudoku Pro, in my terminology!  It’s also why it has solid cages, rather than dashed-line cages).

The logic isn’t too tricky, but for speed you might find a calculator helps you make a few of the logically easy deductions…

Good luck!

## Killer CalcuDoku +/-

Killer CalcuDoku +/- 6×6 puzzle

There’s a lot of very interesting puzzle space to explore between the extremes of Killer Sudoku and KenKen (a trademark of Nextoy LLC, so I will always refer to this as CalcuDoku from now on, unless anyone suggests a better name!).

I’m going to define two in-between puzzles, giving a continuum like this:

1. Killer Sudoku
2. Killer Sudoku Pro – Killer Sudoku with extra operations (+, -, x, /)
3. Killer CalcuDoku – Killer Sudoku Pro with repeated digits in cages, like CalcuDoku
4. CalcuDoku – Killer CalcuDoku puzzles without box constraints (e.g. no 3×3 boxes)

To avoid confusion I’m going to draw Killer Sudoku and CalcuDoku the way they always are – with dashed-line cages in the first case and bold lines between squares for the latter (replacing the traditional Sudoku bold lines).  Then to distinguish the others, Killer Sudoku Pro will appear exactly like Killer Sudoku except that there will be additional operators within the grid (for operator-less ones I’ll include a question mark “?” or similar after each clue).  Killer CalcuDoku, meanwhile, will appear exactly like today’s puzzle – with solid cages within the main puzzle.

Now just to spice things up further, I’m going to mess around with how the puzzles work.  Remember that the key difference between Sudoku and Killer Sudoku is that the digits now actually have value as well – so by fiddling with those values we can create an infinite range of new puzzles that solve in quite different ways.

Example Killer CalcuDoku +/- solution

Today is a good example: here’s a 6×6 +/- Killer CalcuDoku.  The aim is to place -3, -2, -1, 1, 2 and 3 into each row, column and 2×3 bold-lined box, and to place numbers so that the inner cages compute to the value given when applying the stated operation to the set of numbers in that cage.  Subtraction and division are again defined as starting with the highest number in that cage (so remember that 2>-3!) and then applying all the other numbers in any order – so for example the solution to a “4-” cage could be “1 and -3″.  Confused?  See, I said it would mix things up! (1 – -3 = 4)

I’ve included an example (trivial) 4×4 Killer CalcuDoku +/- solution so you can be sure you understand how it works.  But you might not need it – it’s actually a very gentle puzzle I’ve attached, as you’ll probably soon find out… (well, once you get your head around the negative numbers!)

Good luck!

## Killer Sudoku Pro / All Signs

Killer Sudoku All Signs puzzle

Here’s a Killer Sudoku with “all the signs”, or Killer Sudoku Pro if you prefer.  If you’ve got any ideas for a better name let me know!

As in a regular Killer puzzle, you can’t repeat a digit within the solution to any cage.  Unlike in a regular Killer, all non-single cages specify the operation that is applied to produce the result given.  If the operation is + or x then just add or multiply all the digits to give that total.  For subtraction and division you must start with the largest number in the region and subtract or divide the other numbers from that to give the stated result (this is what you’d do intuitively, I think, but since these operations aren’t commutative it’s necessary to state this!)  Other than that, regular Sudoku rules apply: place 1 to 9 into each row, column and bold-lined 3×3 box.

The logic is once again simple, as a first example of this puzzle type, but I think the wider range of operations brings a freshness to the puzzle.  Let me know if you agree (or disagree!).

Good luck!

## Killer Sudoku Multiplication

I thought it would be interesting to see what a Killer Sudoku puzzle would look like if every operation in it was multiplication, so I decided to try it out.

The puzzles attached aren’t labelled with ‘x’ signs, but it should be fairly obvious from the totals that addition is not enough!  Single-cell regions are simply equal to the stated value, but in all others you must multiply all of the cell values together to give the total at the top-left.  Note that this follows Killer Sudoku rules, so a number cannot be repeated within a region.

These are all definitely rated ‘gentle’ – the logic required is simple, even though the multiplication might appear intimidating! In actual fact you don’t need to calculate most of the big values – try the 6×6 puzzle first to see why this is.

Good luck!

PS Subtraction and division are less interesting, unless you allow negative or fractional numbers!  I’ll probably post examples of both the next couple of days anyway however!