# Sandwich Sudoku Puzzles

Of the many sudoku variants that exist, sandwich sudoku is one of the most intriguing. There are at least two different sudoku variants known by this name:

1) A puzzle where one-or-more numbers may be given outside the grid at the start or end of rows/columns. In this variant, the number 8 at the start of a row would mean that the 8 was sandwiched between other numbers that sum up to 8 (583, for instance, or 682 or 781 in some order).

2) A puzzle where numbers are given at the start or end of every row/column, and these numbers indicate the sum of the values between the 1 and 9 in that row or column (or 1 and 6, for a 6x6 sudoku)

In this article, we are focusing on the second of these sudoku variants known as sandwich sudoku, which you may also have come across under names such as between-1-and-9 sudoku or between-1-and-6-sudoku. These drier-sounding names indicate more clearly how the tasty puzzle works.

The appeal of sandwich sudoku is that there are many different pieces of solving logic that it introduces, and some of these are quite subtle. The more puzzles you tackle, the more you realise how much 'sandwich logic' can be applied, and it is integral to the solve of the puzzle. This contrasts with some variants where the new logic either isn't particularly interesting, isn't actually used a great deal, or doesn't have much depth.

Familiarity with totals that can sum to given numbers, as with kakuro and killer sudoku, is very important to making progress with these puzzles. In a 9x9 sandwich Sudoku (or any other size), the smallest number that can appear outside the grid is 0, this means that the 1 and 9 are adjacent in the grid. If you know where one of them is, you know where the other is. If you have 1 as a candidate for the first square in a row whose sandwich value is 0, but the second square doesn't have 9 as a candidate, then you know the first square doesn't contain a 1.

The highest sandwich score for a 9x9 sandwich sudoku is 35. This is the sum of the numbers 2,3,4,5,6,7,8. Therefore if you see a 35 outside a row or column, then you can place 1/9 as the only candidates for the first and last squares in that region.

Knowing how big a sandwich can be is sometimes key to making progress with sandwich sudoku puzzles, not just in the extreme cases but lots of intermediate ones, too. When solving a sandwich sudoku, usually the first thing you need to do to make progress is to work out where the 1s and 9s can go in as many regions as possible. Therefore you'll need to consider cases where you know where one is in a region but not the other, and also cases where you don't know where either are. If a 1 and a 9 are placed already in a region, then you can consider what values can be placed between them to make the required sum, and often make further progress by doing so.

If you'd like to have a go at a sandwich Sudoku puzzle, then you can play the Sandwich Sudoku Puzzle shown above-right on this page. The solution is on the second page of the PDF, we hope you enjoy it.

Remember to use the tips above to help you work out where the 1s and 9s can go in each region to help you get started. For instance, look at the 9 in column two. You can use the position of the 9 and 7 in the column, together with the sandwich total of 11, to place the digits immediately above and below the 7 straightaway. Can you see why, and what they are?

Do you like sandwich sudoku? Have you found any useful solving tips or tricks you'd like to share? Feel free to post your thoughts about sandwich sudoku below.

*Date written: 18 May 2019*

Category: sudoku

Keywords: Sudoku | sandwich **Comment on this post**

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