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Sandwich Sudoku

Sum between the 1 and the 9. Free, at five levels.

Explore hand-set puzzles2,600+ from 600 setters

How to play sandwich sudoku

Sandwich sudoku puts numbers outside the grid. Each one is the sum of the digits between the 1 and the 9 in that row or column, the filling of the sandwich.

A clue of 0 means the 1 and 9 are next to each other, and a clue of 35 means they sit at the two ends. Most solves start by working out how far apart the 1 and 9 can be.

Sandwich sudoku: full lesson

Sandwich Sudoku rule explained in one short example

See the rule in 15 seconds

At a glance

A clue outside the grid sums the digits between 1 and 9.
1 and 9 themselves don't count.
A clue of 0 means 1 and 9 are next to each other.
The biggest clue is 35, with 1 and 9 at the two ends.

Sandwich sums

Every sandwich total, how many cells can sit between 1 and 9, and which digits from 2 to 8 can make it. Totals with one combination are highlighted. Use the finder to filter by digits you already know.

Total

Tap a digit once if it must be in, twice to leave it out

Every sandwich total 0 to 35

Total	Cells between	Possible fillings
0	0	–
1	none	Impossible
2	1	2
3	1	3
4	1	4
5	1, 2	5 23
6	1, 2	6 24
7	1, 2	7 25 34
8	1, 2	8 26 35
9	2, 3	27 36 45 234
10	2, 3	28 37 46 235
11	2, 3	38 47 56 236 245
12	2, 3	48 57 237 246 345
13	2, 3	58 67 238 247 256 346
14	2, 3, 4	68 248 257 347 356 2345
15	2, 3, 4	78 258 267 348 357 456 2346
16	3, 4	268 358 367 457 2347 2356
17	3, 4	278 368 458 467 2348 2357 2456
18	3, 4	378 468 567 2358 2367 2457 3456
19	3, 4	478 568 2368 2458 2467 3457
20	3, 4, 5	578 2378 2468 2567 3458 3467 23456
21	3, 4, 5	678 2478 2568 3468 3567 23457
22	4, 5	2578 3478 3568 4567 23458 23467
23	4, 5	2678 3578 4568 23468 23567
24	4, 5	3678 4578 23478 23568 24567
25	4, 5	4678 23578 24568 34567
26	4, 5	5678 23678 24578 34568
27	5, 6	24678 34578 234567
28	5, 6	25678 34678 234568
29	5, 6	35678 234578
30	5, 6	45678 234678
31	6	235678
32	6	245678
33	6	345678
34	none	Impossible
35	7	2345678

A dash means no filling: the 1 and 9 sit side by side. The gap between 1 and 9 is one more than the number of filling cells.

How to start a sandwich sudoku

Read the extreme clues
0 means 1 and 9 touch, and 35 means they're at the two ends with 2 to 8 between. 2, 3 and 4 can each only be one digit. The sums table shows every other total.
Count the gap
Each total allows only some sandwich lengths. A total of 5 is 5 alone or 2 + 3, so 1 and 9 are two or three cells apart.
Place 1 and 9 together
In each row and column, 1 and 9 are the bread. Where the gap is fixed, they can only sit in a few spots, and those spots interact with the columns.
Fill the filling
Once the bread is placed, the filling is a cage with a known total, so killer combinations take over. The killer combination chart helps.
Work rows and columns together
A 1 or 9 placed by a row clue is also bread for its column. Most sandwich solves bounce between the two.

Common mistakes

Counting 1 or 9 in the sum

Only the digits between them count, never the bread.

Fixing the order

The 1 can be on either side of the 9. The clue says nothing about which comes first.

Forgetting rows without clues

No clue means no information, not a sum of 0.

Five levels, no guessing

Every puzzle has one solution, proved when it is set, and our solver finishes it by logic alone. The level is the hardest step the solve needs. Here is what each level asks of a sandwich puzzle:

The daily variant rotates through 11 kinds, so a sandwich daily comes round about every 11 days. Past dailies

Hand-set sandwich puzzles

Our levels are a good start. For more, Explore has 78 sandwich puzzles made by people, from Logic Masters and Cracking the Cryptic. A few of the most popular: