Cross Sums / Kakuro – Puzzle 1, Step 3 (Easy)

We’ll solve for A.  First we will find the possibilities for A by the row and then A by the column.

A by the Row: Unique combination

According to A’s column:  A+B= 4
The only possible combination for A and B are 3 and 1 (in some order).

Possible values for A by the row:

By:	1	2	3	4	5	6	7	8	9
Row		NO		NO	NO	NO	NO	NO	NO

A by the Column: Lowest Possible – 2 Cells

According to A’s Column: A+D = 12

If A was 2, then D would have to be 10 and that is not possible.  So A is 3 or greater. The LOWEST possible value for A or D is 3.

Possible Values for A by the column are:

By:	1	2	3	4	5	6	7	8	9
Column	NO	NO

Solve for A: Combine Row and Column Possibilities

Combine column possibilities (A = 1 or 3) and row possibilities (A >= 3).  The only value that would make both of these possible is A=3

By:	1	2	3	4	5	6	7	8	9
Row		NO		NO	NO	NO	NO	NO	NO
Column	NO	NO
Both	NO	NO	YES	NO	NO	NO	NO	NO	NO

So A=3

Solve B,C,D,E: Complete Sums

Solve B:    A+B = 4;        3+B=4;         B=4-3;        B=1
Solve D:   A+D=12;        3+D=12;      D=12-3;     D=9
Solve C:   B+C=9;          1+C=9;         C=9-1;        C=8
Solve E:  C+D+E=19;    8+9+E=19;  E=19-8-9;   E=2