## Sudoku Cluster

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Sudoku Cluster

Sudoku Cluster is a logic-based number-placement puzzle. It is distinct from but shares some properties and rules with Sudoku and kenken

Rules:
• All classic Sudoku rules apply
• Some cells have numbers written on the top-left corner, Let's call them cluster-heads
• Divide the board into clusters such that
• Each cell belongs to one and only one cluster
• Each cluster has one and only one cluster head
• The summation of the numbers in each cluster must be equal to the number in the cluster head

Cluster Sudoku is like Kenken, with the following differences:
• clusters are not given
• cluster are either horizontal or vertical
• the only operation is add

Below is a solved puzzle:

ClusterSudoku_sample001_Solution.png (34.58 KiB) Viewed 329 times

And here is a sample for you to solve:

ClusterSudoku_sample002_Problem.png (10.86 KiB) Viewed 329 times

Posts: 77
Joined: 31 July 2019

### Re: Sudoku Cluster

Another nice idea, Kousha ... looks like it could be fun!

A possible variant might be a "mystery cluster" - one sum clue is omitted - we can work out what that sum is, but the mystery is where to put it ...

Mathimagics
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Location: Canberra

### Re: Sudoku Cluster

Thank's for this, I'll try it.

Note it is a variant on Killer Un-caged published in the UK Sunday Telegraph.
For Mathimagics' suggestion of unknown sums see my posts on the Assassin site, for example:
http://www.rcbroughton.co.uk/sudoku/for ... e3443b8f32
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

### Re: Sudoku Cluster

HATMAN wrote:Thank's for this, I'll try it.

Note it is a variant on Killer Un-caged published in the UK Sunday Telegraph.
For Mathimagics' suggestion of unknown sums see my posts on the Assassin site, for example:
http://www.rcbroughton.co.uk/sudoku/for ... e3443b8f32

Could you please send me the link to the "Killer Un-caged"?

Posts: 77
Joined: 31 July 2019

### Re: Sudoku Cluster

Mathimagics wrote:Another nice idea, Kousha ... looks like it could be fun!

A possible variant might be a "mystery cluster" - one sum clue is omitted - we can work out what that sum is, but the mystery is where to put it ...

Could you please elaborate?

Posts: 77
Joined: 31 July 2019

### Re: Sudoku Cluster

Unfortunately the Sunday Telegraph online site does not publish the uncaged killers - they are only in the physical paper.

I only get them when I'm in England but I put a couple of them on the assassin site (I had to make them harder as newspaper puzzles are normally too easy - this was where I got the idea of question marks instead of numbers).
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

### Re: Sudoku Cluster

HATMAN wrote:Unfortunately the Sunday Telegraph online site does not publish the uncaged killers - they are only in the physical paper.

I only get them when I'm in England but I put a couple of them on the assassin site (I had to make them harder as newspaper puzzles are normally too easy - this was where I got the idea of question marks instead of numbers).

Thanks HATMAN,

I found some samples https://www.puzzler.com/puzzles-a-z/killer-uncaged

What I've designed is quite similar but not the same, in my version the sum of a cage can appear in any cell of the cape, while in uncaged killers "The sum of the digits for each missing cage (or inner shape) is placed, as usual, in the leftmost cell of the top row of that cage."

I didn't know about uncaged killers when designing my version

Posts: 77
Joined: 31 July 2019

### Re: Sudoku Cluster

I've just started solving your one and clearly the cage placement process is quite different.

I'll let you know my views when finished.

Thank you for the reference.
They state that the only other rule is no single cages but from more general killers they also need:
1. no uncovered cells (however the total of the sums infers this)
2. no overlapping cages
3. no diagonally connected cages
4. no remote cages (i.e. a set of unconnected cells)
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

### Re: Sudoku Cluster

HATMAN wrote:I've just started solving your one and clearly the cage placement process is quite different.

I'll let you know my views when finished.

Thank you for the reference.
They state that the only other rule is no single cages but from more general killers they also need:
1. no uncovered cells (however the total of the sums infers this)
2. no overlapping cages
3. no diagonally connected cages
4. no remote cages (i.e. a set of unconnected cells)

In my case, the same rules apply, and the cages are either horizontal or diagonal, which is more restrictive

Posts: 77
Joined: 31 July 2019

### Re: Sudoku Cluster

Kousha: I forgot to respond to your request for elaboration on the "mystery cluster" idea.

This simply means that for one of the clusters you don't give the sum-clue. While the sum itself is easily determined, the cell location information is hidden, so this would tend to make the puzzle harder.

Mathimagics
2017 Supporter

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Joined: 27 May 2015
Location: Canberra

### Re: Sudoku Cluster

Kousha

I'm not finished yet, but I'm really enjoying the solving process.

This is not a variant of uncaged killer. Both are different puzzles in the class Boundary (placement) Killers.

Please post this on the Assassin site as well. As it has givens I suggest in the Variants section.

Maurice
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

### Re: Sudoku Cluster

Mathimagics wrote:Kousha: I forgot to respond to your request for elaboration on the "mystery cluster" idea.

This simply means that for one of the clusters you don't give the sum-clue. While the sum itself is easily determined, the cell location information is hidden, so this would tend to make the puzzle harder.

I still don't get it, can you sketch it?

Posts: 77
Joined: 31 July 2019

### Re: Sudoku Cluster

HATMAN wrote:Kousha

I'm not finished yet, but I'm really enjoying the solving process.

This is not a variant of uncaged killer. Both are different puzzles in the class Boundary (placement) Killers.

Please post this on the Assassin site as well. As it has givens I suggest in the Variants section.

Maurice

Assassin site? could you please elaborate?

Posts: 77
Joined: 31 July 2019

### Re: Sudoku Cluster

Take your "Sample002_Problem" above. In r9c6 you have the clue "12".

Remove that clue! Now, is the solution still unique? If so, you have a "mystery cluster" puzzle. If not, try removing other sums.

Mathimagics
2017 Supporter

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Joined: 27 May 2015
Location: Canberra

### Re: Sudoku Cluster

Kousha

Richard's site at:
http://www.rcbroughton.co.uk/sudoku/for ... 6dcd994df0

It is the home site for very hard killers named Assassins by Ruud long ago.

Maurice
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

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