Cross Sums / Kakuro – Puzzle 1, Step 4 (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 Row: Lowest Possible – 2 Cells

According to A’s row: A+C = 12

If A was 2, then C would have to be 10 and that is not possible.  So A is 3 or greater. The LOWEST possible value for A or C 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 row possibilities (A = 1 or 3) and column 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 Complete Sums

Solve B:    A+B=4;       3+B=4;         B=4-3;          B=1
Solve C:    A+C=12;     3+C=12;       C=12-3;        C=9

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

Cross Sums / Kakuro – Puzzle 1, Step 2 (Easy)

Let’s move our attention up slightly:

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

A by the Column: Unique combination

According to A’s column:  A+C = 3
The only possible combination for A and C are 2 and 1 (in some order).

Possible values for A by the column:

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

A by the Row: Lowest Possible – 2 Cells

According to A’s row: A+B = 11

If A was 1, then B would have to be 10 and that is not possible.  So A is 2 or greater. The LOWEST possible value for A or B is 2.

Possible Values for A by the row are:

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

Solve for A: Combine Row and Column Possibilities

Combine column possibilities (A = 1 or 2) and row possibilities (A >= 2).  The only value that would make both of these possible is A=2.

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

So A=2.

Solve B,C,D,E: Complete Sums

Solve B:    A+B=11;       2+B=11;      B=11-2;     B=9
Solve C:    A+C=3;         2+C=3;        C=3-2;        C=1
Solve D:   B+D=11;       9+D=11;     D=11-9;      D=2
Solve E:   C+D+E=11;  1+2+E=11;  E=11-2-1;   E=8

Cross Sums / Kakuro / Puzzle 1 / Step 1 (Easy)

Logic Reasoning 1: Unique Combination
According to A’s column:  A+D = 3
The only possible combination for D and A are 2 and 1 (in some order).

Possible values for A:

1	2	3	4	5	6	7	8	9
		NO	NO	NO	NO	NO	NO	NO

Logic Reasoning 2: Lowest Possible Value – 2 Cells
According to A’s row: A+B = 11

If A was 1, then B would have to be 10 and that is not possible.  So A is 2 or greater. The LOWEST possible value for A or B is 2.

Possible Values for A:

1	2	3	4	5	6	7	8	9
NO

Logic Reasoning 3: Combine Row and Column Possibilities

Combine Logic reasoning 1 (A = 1 or 2) and Logic reasoning 2 (A >= 2).  The only value that would make both of these possible is A=2.

	1	2	3	4	5	6	7	8	9
Row (1)			NO	NO	NO	NO	NO	NO	NO
Col (2)	NO
Both (3)	NO		NO	NO	NO	NO	NO	NO	NO

So A=2.

Logic Reasoning 4: Complete Sums

Solve B:     A + B = 11;    2 + B = 11;    B = 11 – 2;   B = 9
Solve D:    A+D = 3;        2+D = 3 ;       D=3-2;          D=1
Solve C:    C+B=12;         C+9=12;        C=12-9;        C=3
Solve E:    E+D+C=13;    E+1+3 =13;   E=13-3-1;    E=9
Solve F:    F+E =12;        F+9=12;         F=12-9;       F=3
Solution:

Cross Sums / Kakuro / Puzzle 1 / Step 1a (Easy)

We will start with the section in the lower right:

Cross Sum / Kakuro Puzzle #1 (Easy)

We’ll step through the following cross sum (Kakuro)  puzzle step-by-step. This puzzle is easy level.

	17	17		3	29		15	8		17	9
9			6 15			3			3 12
32						34 7
	10 7			11				4			6
3			11	23 12				3	4 23
28					38	15	19 21
	9	28 12								11	3
19				23 11				11 5
4			16 8			9
	11	6 4				6 14				3	12
11				20				13
11				12					11