The most important trick to
solving the first stage of Suduro puzzles is to
recognize that the each gray cell belongs to three restricted sets, the set of
gray cells that share its column, the set of gray cells that share its row, and
the set of gray squares that share its subgrid. Each of the three sum clues
that apply to each cell potentially restricts the set of numbers that might
work in that cell, and as you solve for some of the cells, you gain further
information, as you rule out numbers in the columns, rows, and subgrids, and
as you solve for portions of the sums. For example, consider the gray cell
(with an asterisk) at the center of the following partial puzzle as example:




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14 




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The number in the center
square simultaneously belongs to three sets, the set of numbers that can add up
to 14, in a twocell sum (for the row clue), the set of numbers that can add up
to 7 in a twocell sum (for the column clue), and the set of numbers that can
add up to 10 in a twocell sum (for the subgrid clue). Since the other cell in
the row cannot be larger than 9, 5 is the smallest number consistent with the
row sum of 14. Since the other cell in the column cannot be less than 1, 6 is
the largest number consistent with the column sum of 7. So far, the row and
column clues taken together restrict possible values for the center square to
just the numbers 5 and 6. Finally, taking the subgrid sum of 10, we know that
neither gray cell in the center subgrid can be a 5 because if one was a 5, the
other would also have to be a 5 to make the center subgrid gray cells sum to
10, but repeats are not allowed. Therefore, taking all three sum clues for the
center cell, together, the only possible value for the center cell remaining is
6, and you could confidently fill in that square with no guessing the overlap
of the three sets that the center cell must belong to contains just a single
number.
This is very similar to the
logic you probably already use for row and column clues in Kakuro,
if you are an experienced Kakuro solver, but you must
remember that with Suduro, each cell has three clues, thanks to the subgrid
sums, and you may find the necessary deductions with any combination of these
three clues, with roughly equal likelihood. (I considered using just row and
column clues for Suduro, when creating the rules for Suduro, to more closely mimic Kakuro,
but there are two reasons I added subgrid clues:
Where rows, columns and
subgrids often contain more than 2 gray cells (3 is roughly average, in Suduro, at the beginning of the solution), it requires
quite a lot of mental arithmetic to work out the allowed values, for each of
the three sets, for each of the gray cells in the puzzle, until you get used to
the recurring patterns. (The same is true for solving Kakuros.)
Some people find it helpful to refer to tables of required and allowed values
for potential sums. Here are the tables that work out these restrictions for
you:
2Cell Sums 


Sum 
Restrictions 

3 
1,2 

4 
1,3 

5 
≤4 

6 
≤5,≠3 

7 
≤6 

8 
≤7,≠4 

9 
≤8 

10 
≠5 

11 
≥2 

12 
≥3,≠6 

13 
≥4 

14 
≥5,≠7 

15 
≥6 

16 
7,9 

17 
8,9 

3Cell sums 


Sum 
Restrictions 

6 
1,2,3 

7 
1,2,4 

8 
1,≤5 

9 
≤6 

10 
≤7 

11 
≤8 

1218 
any 

19 
≥2 

20 
≥3 

21 
≥4 

22 
9,≥5 

23 
6,8,9 

24 
7,8,9 

4Cell Sums 


Sum 
Restrictions 

10 
1,2,3,4 

11 
1,2,3,5 

12 
1,2,≤6 

13 
1,≤7 

14 
≤8 

1525 
any 

26 
≥2 

27 
9,≥3 

28 
8,9,≥4 

29 
5,7,8,9 

30 
6,7,8,9 

5Cell
Sums 


Sum 
Restrictions 

15 
1,2,3,4,5 

16 
1,2,3,4,6 

17 
1,2,3,≤7 

18 
1,2,≤8 

19 
1,any 

2030 
any 

31 
9,any 

32 
8,9,≥2 

33 
7,8,9,≥3 

34 
4,6,7,8,9 

35 
5,6,7,8,9 

6Cell Sums 


Sum 
Restrictions 

21 
1,2,3,4,5,6 

22 
1,2,3,4,5,7 

23 
1,2,3,4,≤8 

24 
1,2,3,any 

25 
1,2,any 

26 
1,any 

2733 
any 

34 
9,any 

35 
8,9,any 

36 
7,8,9,any 

37 
6,7,8,9,≥2 

38 
3,5,6,7,8,9 

39 
4,5,6,7,8,9 

7Cell Sums 


Sum 
Restrictions 

28 
1,2,3,4,5,6,7 

29 
1,2,3,4,5,6,8 

30 
1,2,3,4,5,any 

31 
1,2,3,4,7,any 

32 
1,2,3,any 

33 
1,2,6,any 

34 
1,any 

35 
≠5 

36 
9,any 

37 
4,8,9,any 

38 
7,8,9,any 

39 
3,6,7,8,9,any 

40 
5,6,7,8,9,any 

41 
2,4,5,6,7,8,9 

42 
3,4,5,6,7,8,9 

8Cell Sums 


Sum 
Restrictions 

36 
All except 9 

37 
All except 8 

38 
All except 7 

39 
All except 6 

40 
All except 5 

41 
All except 4 

42 
All except 3 

43 
All except 2 

44 
All except 1 

9Cell
Sum 


Sum 
Restrictions 

45 
All 

Very likely these tables
look confusing at first, so let me walk through them and explain what they say.
Numbers in bold and underlined
are required for that sum. Therefore, for example, 1 and 3 are both absolutely
required for a legal sum of two numbers equaling 4, from the second row of the
first table. (2 and 2 are not allowed because duplicates are not allowed.)
Plaintext restrictions (not underlined, not in bold text) are further restrictions that apply to all the numbers
in the sum. For example, any number participating in a twonumber sum of 5 must
be less than or equal to 4 (≤4), according to the third row in the first
table, and all numbers in a twonumber sum of 10 must not be equal to 5 (≠5)
(else youd need duplicates). The restriction any simply means that any
number can participate in that sum. Where you have both bold and underlined restrictions, and other restrictions as well, we know some
numbers precisely, but not all. For example, the threecell sum of 8 (from the
third row of the second table) must contain a 1, but all we know about the other two numbers in the sum is
that they are ≤5 (and leave a sum of 8, of course).
Even understanding how to
read these tables, they may still seem intimidating, but there are tricks to
get past this. First, youll almost never find 6 or more cells in a sum in Suduro, so you can pretty well ignore the second row of
tables. (These are useful in Kakuro, though, where
such manycell sums come up more often.) Also, you can learn to quickly derive
the most useful restrictions in your head if you remember just a few facts and
rules:
Here is the short table of
highest and lowest possible sums that makes the above rules easy to apply
remember these 8 numbers, and then you can work out the rest of what you need
quickly in your head:
# of
Cells 
Lowest
Sum 
Highest
Sum 
2 
3 
17 
3 
6 
24 
4 
10 
30 
5 
15 
35 
So far, Ive shown how to
reduce the possible values for certain cells to just a single value at the very
beginning of solving stage 1, before you have found any other values, and this
is important, because getting started is sometimes the hardest part. Once you
fill in a few numbers, though, the sum clues become even more useful. For
example, consider the following partly solved partial puzzle:




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Using Trick 2 (see here), we find the 3 in the cell shown. Previously, based
on the column clue shown, we knew that cell a was 1, 2, or 3, and based
on the subgrid clue shown, we knew that all gray cells in that subgrid were ≤5,
and that at least one of the cells was a 1. Once we fill in the 3, however, we
can find the exact values of a and b
fairly easily. One approach is to recognize that the two unknown cells must sum
to 5 (83), and that since one of these cells must be a 1, the other must be a
4. Further, since a can be only a 1, 2, or 3 (based on the column clue), a
must be 1, and b must be 4. Even if we forgot that one of the cells in that
subgrid must be a 1, we could quickly deduce the fact, since a+b=5, leaving just the combinations (1,4)
and (2,3), but they cannot be 2 and 3, since we already have a 3 in the
subgrid. (Quickly finding the pairs of numbers that add to something is easy:
for numbers less than 11, start with 1 and another number (for example, (1,8)
for the sum of 9), and work your way inward (for example, for the sum of 9,
find the pairs (1,8), (2,7), (3,6), (4,5)). For sums greater than 10, start with
a pair using 9 and work your way inward (for example, for the sum of 12, find
the pairs (3,9), (4,8), (5,7)).
Sometimes, you have to
follow a chain of reasoning to deduce the value in a single square at the
beginning of a puzzle. For example, below, note that a must be 8 or 9, since
the two gray squares in that row sum to 17. This means, in turn, that b must be
1 or 2, since a+b=10, according to
the center subgrid clue. Therefore, c must be 5 or 6 to satisfy the row
clue, b+c=7, but c
may not be 6, since c+d=12, and c≠d, which just leaves c=5.
(This also allows us quickly to work out that d=7, b=2, a=8, among others.)




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