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Killer Combinations

Each clue in each cage will give rise to a certain set of combinations of numbers for each cell. It is a convention of Killer Sudoku that no cage will duplicate a number (even if it dog-legs through several 3 by 3 boxes).

Some cages will not be very helpful but certain combinations, such as these listed here mean that the total number of possible numbers is equal to the cage size. In the first, for example, a clue of 3 in a cage of size 2 can only have 1 and 2 in it. These means you can remove 3 to 9 from those cells.

I have written an example of the use of 'hard' Killer combinations on this page.


ClueCage SizeCombinations
321,2
421,3
1627,9
1728,9
631,2,3
731,2,4
2336,8,9
2437,8,9
1041,2,3,4
1141,2,3,5
2945,7,8,9
3046,7,8,9
1551,2,3,4,5
1651,2,3,4,6
3454,6,7,8,9
3555,6,7,8,9
2161,2,3,4,5,6
2261,2,3,4,5,7
3863,5,6,7,8,9
3964,5,6,7,8,9
2871,2,3,4,5,6,7
2971,2,3,4,5,6,8
4172,4,5,6,7,8,9
4273,4,5,6,7,8,9
Any81-9 except 45
minus clue value
Any91-9 inclusive

The absolutely exhaustive combination of all cage clues, cage sizes
and the combination of combinations for those cage size/values is:


Cage SizeCage ValueCombinationCombos Combined
231/2Unique
241/3Unique
251/4
252/31/2/3/4
261/5
262/41/2/4/5
271/6
272/5
273/41/2/3/4/5/6
281/7
282/6
283/51/2/3/5/6/7
291/8
292/7
293/6
294/51/2/3/4/5/6/7/8
2101/9
2102/8
2103/7
2104/61/2/3/4/6/7/8/9
2112/9
2113/8
2114/7
2115/62/3/4/5/6/7/8/9
2123/9
2124/8
2125/73/4/5/7/8/9
2134/9
2135/8
2136/74/5/6/7/8/9
2145/9
2146/85/6/8/9
2156/9
2157/86/7/8/9
2167/9Unique
2178/9Unique
361/2/3Unique
371/2/4Unique
381/2/5
381/3/41/2/3/4/5
391/2/6
391/3/5
392/3/41/2/3/4/5/6
3101/2/7
3101/3/6
3101/4/5
3102/3/51/2/3/4/5/6/7
3111/2/8
3111/3/7
3111/4/6
3112/3/6
3112/4/51/2/3/4/5/6/7/8
3121/2/9
3121/3/8
3121/4/7
3121/5/6
3122/3/7
3122/4/6
3123/4/51/2/3/4/5/6/7/8/9
3131/3/9
3131/4/8
3131/5/7
3132/3/8
3132/4/7
3132/5/6
3133/4/61/2/3/4/5/6/7/8/9
3141/4/9
3141/5/8
3141/6/7
3142/3/9
3142/4/8
3142/5/7
3143/4/7
3143/5/61/2/3/4/5/6/7/8/9
3151/5/9
3151/6/8
3152/4/9
3152/5/8
3152/6/7
3153/4/8
3153/5/7
3154/5/61/2/3/4/5/6/7/8/9
3161/6/9
3161/7/8
3162/5/9
3162/6/8
3163/4/9
3163/5/8
3163/6/7
3164/5/71/2/3/4/5/6/7/8/9
3171/7/9
3172/6/9
3172/7/8
3173/5/9
3173/6/8
3174/5/8
3174/6/71/2/3/4/5/6/7/8/9
3181/8/9
3182/7/9
3183/6/9
3183/7/8
3184/5/9
3184/6/8
3185/6/71/2/3/4/5/6/7/8/9
3192/8/9
3193/7/9
3194/6/9
3194/7/8
3195/6/82/3/4/5/6/7/8/9
3203/8/9
3204/7/9
3205/6/9
3205/7/83/4/5/6/7/8/9
3214/8/9
3215/7/9
3216/7/84/5/6/7/8/9
3225/8/9
3226/7/95/6/7/8/9
3236/8/9Unique
3247/8/9Unique
4101/2/3/4Unique
4111/2/3/5Unique
4121/2/3/6
4121/2/4/51/2/3/4/5/6
4131/2/3/7
4131/2/4/6
4131/3/4/51/2/3/4/5/6/7
4141/2/3/8
4141/2/4/7
4141/2/5/6
4141/3/4/6
4142/3/4/51/2/3/4/5/6/7/8
4151/2/3/9
4151/2/4/8
4151/2/5/7
4151/3/4/7
4151/3/5/6
4152/3/4/61/2/3/4/5/6/7/8/9
4161/2/4/9
4161/2/5/8
4161/2/6/7
4161/3/4/8
4161/3/5/7
4161/4/5/6
4162/3/4/7
4162/3/5/61/2/3/4/5/6/7/8/9
4171/2/5/9
4171/2/6/8
4171/3/4/9
4171/3/5/8
4171/3/6/7
4171/4/5/7
4172/3/4/8
4172/3/5/7
4172/4/5/61/2/3/4/5/6/7/8/9
4181/2/6/9
4181/2/7/8
4181/3/5/9
4181/3/6/8
4181/4/5/8
4181/4/6/7
4182/3/4/9
4182/3/5/8
4182/3/6/7
4182/4/5/7
4183/4/5/61/2/3/4/5/6/7/8/9
4191/2/7/9
4191/3/6/9
4191/3/7/8
4191/4/5/9
4191/4/6/8
4191/5/6/7
4192/3/5/9
4192/3/6/8
4192/4/5/8
4192/4/6/7
4193/4/5/71/2/3/4/5/6/7/8/9
4201/2/8/9
4201/3/7/9
4201/4/6/9
4201/4/7/8
4201/5/6/8
4202/3/6/9
4202/3/7/8
4202/4/5/9
4202/4/6/8
4202/5/6/7
4203/4/5/8
4203/4/6/71/2/3/4/5/6/7/8/9
4211/3/8/9
4211/4/7/9
4211/5/6/9
4211/5/7/8
4212/3/7/9
4212/4/6/9
4212/4/7/8
4212/5/6/8
4213/4/5/9
4213/4/6/8
4213/5/6/71/2/3/4/5/6/7/8/9
4221/4/8/9
4221/5/7/9
4221/6/7/8
4222/3/8/9
4222/4/7/9
4222/5/6/9
4222/5/7/8
4223/4/6/9
4223/4/7/8
4223/5/6/8
4224/5/6/71/2/3/4/5/6/7/8/9
4231/5/8/9
4231/6/7/9
4232/4/8/9
4232/5/7/9
4232/6/7/8
4233/4/7/9
4233/5/6/9
4233/5/7/8
4234/5/6/81/2/3/4/5/6/7/8/9
4241/6/8/9
4242/5/8/9
4242/6/7/9
4243/4/8/9
4243/5/7/9
4243/6/7/8
4244/5/6/9
4244/5/7/81/2/3/4/5/6/7/8/9
4251/7/8/9
4252/6/8/9
4253/5/8/9
4253/6/7/9
4254/5/7/9
4254/6/7/81/2/3/4/5/6/7/8/9
4262/7/8/9
4263/6/8/9
4264/5/8/9
4264/6/7/9
4265/6/7/82/3/4/5/6/7/8/9
4273/7/8/9
4274/6/8/9
4275/6/7/93/4/5/6/7/8/9
4284/7/8/9
4285/6/8/94/5/6/7/8/9
4295/7/8/9Unique
4306/7/8/9Unique
5151/2/3/4/5Unique
5161/2/3/4/6Unique
5171/2/3/4/7
5171/2/3/5/61/2/3/4/5/6/7
5181/2/3/4/8
5181/2/3/5/7
5181/2/4/5/61/2/3/4/5/6/7/8
5191/2/3/4/9
5191/2/3/5/8
5191/2/3/6/7
5191/2/4/5/7
5191/3/4/5/61/2/3/4/5/6/7/8/9
5201/2/3/5/9
5201/2/3/6/8
5201/2/4/5/8
5201/2/4/6/7
5201/3/4/5/7
5202/3/4/5/61/2/3/4/5/6/7/8/9
5211/2/3/6/9
5211/2/3/7/8
5211/2/4/5/9
5211/2/4/6/8
5211/2/5/6/7
5211/3/4/5/8
5211/3/4/6/7
5212/3/4/5/71/2/3/4/5/6/7/8/9
5221/2/3/7/9
5221/2/4/6/9
5221/2/4/7/8
5221/2/5/6/8
5221/3/4/5/9
5221/3/4/6/8
5221/3/5/6/7
5222/3/4/5/8
5222/3/4/6/71/2/3/4/5/6/7/8/9
5231/2/3/8/9
5231/2/4/7/9
5231/2/5/6/9
5231/2/5/7/8
5231/3/4/6/9
5231/3/4/7/8
5231/3/5/6/8
5231/4/5/6/7
5232/3/4/5/9
5232/3/4/6/8
5232/3/5/6/71/2/3/4/5/6/7/8/9
5241/2/4/8/9
5241/2/5/7/9
5241/2/6/7/8
5241/3/4/7/9
5241/3/5/6/9
5241/3/5/7/8
5241/4/5/6/8
5242/3/4/6/9
5242/3/4/7/8
5242/3/5/6/8
5242/4/5/6/71/2/3/4/5/6/7/8/9
5251/2/5/8/9
5251/2/6/7/9
5251/3/4/8/9
5251/3/5/7/9
5251/3/6/7/8
5251/4/5/6/9
5251/4/5/7/8
5252/3/4/7/9
5252/3/5/6/9
5252/3/5/7/8
5252/4/5/6/8
5253/4/5/6/71/2/3/4/5/6/7/8/9
5261/2/6/8/9
5261/3/5/8/9
5261/3/6/7/9
5261/4/5/7/9
5261/4/6/7/8
5262/3/4/8/9
5262/3/5/7/9
5262/3/6/7/8
5262/4/5/6/9
5262/4/5/7/8
5263/4/5/6/81/2/3/4/5/6/7/8/9
5271/2/7/8/9
5271/3/6/8/9
5271/4/5/8/9
5271/4/6/7/9
5271/5/6/7/8
5272/3/5/8/9
5272/3/6/7/9
5272/4/5/7/9
5272/4/6/7/8
5273/4/5/6/9
5273/4/5/7/81/2/3/4/5/6/7/8/9
5281/3/7/8/9
5281/4/6/8/9
5281/5/6/7/9
5282/3/6/8/9
5282/4/5/8/9
5282/4/6/7/9
5282/5/6/7/8
5283/4/5/7/9
5283/4/6/7/81/2/3/4/5/6/7/8/9
5291/4/7/8/9
5291/5/6/8/9
5292/3/7/8/9
5292/4/6/8/9
5292/5/6/7/9
5293/4/5/8/9
5293/4/6/7/9
5293/5/6/7/81/2/3/4/5/6/7/8/9
5301/5/7/8/9
5302/4/7/8/9
5302/5/6/8/9
5303/4/6/8/9
5303/5/6/7/9
5304/5/6/7/81/2/3/4/5/6/7/8/9
5311/6/7/8/9
5312/5/7/8/9
5313/4/7/8/9
5313/5/6/8/9
5314/5/6/7/91/2/3/4/5/6/7/8/9
5322/6/7/8/9
5323/5/7/8/9
5324/5/6/8/92/3/4/5/6/7/8/9
5333/6/7/8/9
5334/5/7/8/93/4/5/6/7/8/9
5344/6/7/8/9Unique
5355/6/7/8/9Unique
6211/2/3/4/5/6Unique
6221/2/3/4/5/7Unique
6231/2/3/4/5/8
6231/2/3/4/6/71/2/3/4/5/6/7/8
6241/2/3/4/5/9
6241/2/3/4/6/8
6241/2/3/5/6/71/2/3/4/5/6/7/8/9
6251/2/3/4/6/9
6251/2/3/4/7/8
6251/2/3/5/6/8
6251/2/4/5/6/71/2/3/4/5/6/7/8/9
6261/2/3/4/7/9
6261/2/3/5/6/9
6261/2/3/5/7/8
6261/2/4/5/6/8
6261/3/4/5/6/71/2/3/4/5/6/7/8/9
6271/2/3/4/8/9
6271/2/3/5/7/9
6271/2/3/6/7/8
6271/2/4/5/6/9
6271/2/4/5/7/8
6271/3/4/5/6/8
6272/3/4/5/6/71/2/3/4/5/6/7/8/9
6281/2/3/5/8/9
6281/2/3/6/7/9
6281/2/4/5/7/9
6281/2/4/6/7/8
6281/3/4/5/6/9
6281/3/4/5/7/8
6282/3/4/5/6/81/2/3/4/5/6/7/8/9
6291/2/3/6/8/9
6291/2/4/5/8/9
6291/2/4/6/7/9
6291/2/5/6/7/8
6291/3/4/5/7/9
6291/3/4/6/7/8
6292/3/4/5/6/9
6292/3/4/5/7/81/2/3/4/5/6/7/8/9
6301/2/3/7/8/9
6301/2/4/6/8/9
6301/2/5/6/7/9
6301/3/4/5/8/9
6301/3/4/6/7/9
6301/3/5/6/7/8
6302/3/4/5/7/9
6302/3/4/6/7/81/2/3/4/5/6/7/8/9
6311/2/4/7/8/9
6311/2/5/6/8/9
6311/3/4/6/8/9
6311/3/5/6/7/9
6311/4/5/6/7/8
6312/3/4/5/8/9
6312/3/4/6/7/9
6312/3/5/6/7/81/2/3/4/5/6/7/8/9
6321/2/5/7/8/9
6321/3/4/7/8/9
6321/3/5/6/8/9
6321/4/5/6/7/9
6322/3/4/6/8/9
6322/3/5/6/7/9
6322/4/5/6/7/81/2/3/4/5/6/7/8/9
6331/2/6/7/8/9
6331/3/5/7/8/9
6331/4/5/6/8/9
6332/3/4/7/8/9
6332/3/5/6/8/9
6332/4/5/6/7/9
6333/4/5/6/7/81/2/3/4/5/6/7/8/9
6341/3/6/7/8/9
6341/4/5/7/8/9
6342/3/5/7/8/9
6342/4/5/6/8/9
6343/4/5/6/7/91/2/3/4/5/6/7/8/9
6351/4/6/7/8/9
6352/3/6/7/8/9
6352/4/5/7/8/9
6353/4/5/6/8/91/2/3/4/5/6/7/8/9
6361/5/6/7/8/9
6362/4/6/7/8/9
6363/4/5/7/8/91/2/3/4/5/6/7/8/9
6372/5/6/7/8/9
6373/4/6/7/8/92/3/4/5/6/7/8/9
6383/5/6/7/8/9Unique
6394/5/6/7/8/9Unique
7281/2/3/4/5/6/7Unique
7291/2/3/4/5/6/8Unique
7301/2/3/4/5/6/9 
7301/2/3/4/5/7/81/2/3/4/5/6/7/8/9
7311/2/3/4/5/7/9
7311/2/3/4/6/7/81/2/3/4/5/6/7/8/9
7321/2/3/4/5/8/9
7321/2/3/4/6/7/9
7321/2/3/5/6/7/81/2/3/4/5/6/7/8/9
7331/2/3/4/6/8/9
7331/2/3/5/6/7/9
7331/2/4/5/6/7/81/2/3/4/5/6/7/8/9
7341/2/3/4/7/8/9
7341/2/3/5/6/8/9
7341/2/4/5/6/7/9
7341/3/4/5/6/7/81/2/3/4/5/6/7/8/9
7351/2/3/5/7/8/9
7351/2/4/5/6/8/9
7351/3/4/5/6/7/9
7352/3/4/5/6/7/81/2/3/4/5/6/7/8/9
7361/2/3/6/7/8/9
7361/2/4/5/7/8/9
7361/3/4/5/6/8/9
7362/3/4/5/6/7/91/2/3/4/5/6/7/8/9
7371/2/4/6/7/8/9
7371/3/4/5/7/8/9
7372/3/4/5/6/8/91/2/3/4/5/6/7/8/9
7381/2/5/6/7/8/9
7381/3/4/6/7/8/9
7382/3/4/5/7/8/91/2/3/4/5/6/7/8/9
7391/3/5/6/7/8/9
7392/3/4/6/7/8/91/2/3/4/5/6/7/8/9
7401/4/5/6/7/8/9
7402/3/5/6/7/8/91/2/3/4/5/6/7/8/9
7412/4/5/6/7/8/9Unique
7423/4/5/6/7/8/9Unique
8361/2/3/4/5/6/7/8Unique
8371/2/3/4/5/6/7/9Unique
8381/2/3/4/5/6/8/9Unique
8391/2/3/4/5/7/8/9Unique
8401/2/3/4/6/7/8/9Unique
8411/2/3/5/6/7/8/9Unique
8421/2/4/5/6/7/8/9Unique
8431/3/4/5/6/7/8/9Unique
8442/3/4/5/6/7/8/9Unique



Article created on 12-April-2008. Views: 31836
This page was last modified on 13-April-2014.
All text is copyright and for personal use only but may be reproduced with the permission of the author.
Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2014