Here is a brief walkthrough of the strategies you can employ while solving a Frame Sudoku puzzle. It assumes you are familiar with the basic rules and strategies of classic Sudoku, all of which apply but are not covered here.
First some basic principles and terminology. Each set of three adjoining cells is referred to here as a triplet. Each of the 9 rows in a puzzle has three triplets, likewise each column. The three cells in the triplet to the left of each row have values that sum to the number shown to the left of that row. Same applies to those triplets on the right of each row and for the column triplets at the top and bottom of each column. In the example to the right, the three cells shaded grey must add up to 21.
In solving any Frame Sudoku, it is crucial to know all the combination of three numbers that make up the frame totals. DKM Frame Sudoku has a very useful solve aid - clicking on any frame number will show all possible combinations of that number.
Note that even though the middle triplet in each row and column do not have a total displayed,
you can always calculate its total because all the cells in each row or column always total
45 (1+2+3+4+5+6+7+8+9). So the middle triplet in column 6 (below the yellow one) totals 19 (45 - 6 - 20).
(The Easy puzzles do not utilize this information in their generation.)