Sunday 22 July 2007

Easy time (with hints)

4
1
3
2


And here is a hint to get you started, it is possible to find (or limit to a few candidates) the values for the greyed cells below:
4
1
3
2


When this is done, the value for blue and pink pieces can be found with a bit of logic. At this point, solving the puzzle should not be too hard :)

An easy one

21
2


Hopefully, with the help of yesterday's step-by-step, this one should be easy to solve...

Saturday 21 July 2007

As requested, a step-by-step

Here is a step-by-step for an easy one:
2
26
62
5

First let's start with some simple facts:
- the sum of all cells in a row is 1+2+3+4+5+6 = 21
- the sum of all cells in a column is 21
- because of this the sum of all cells in the puzzle is 6*21. This is also the sum of all pieces (6 blue and 6 pinks ones), so we can deduce that both colors add up to 21.

2
26
62
5?

Now consider the last row. Cells in this row add up to 21. The greyed-out blue and pink pieces too, so we can deduce that the cell with the question mark is a 2.

2
26
62
52

Now add up all cells in the grey area above. This sum is 3*21, but it is also (2 blue pieces) + (4 pink pieces) - 7. This, and the fact that blue and pink add up to 21, leads to the value of blue pieces and pink pieces:
blue = 7, pink = 14.

2
214146
62
52

To complete the first blue piece on row 2, only values 1 and 4 are possible, as shown above.

2?
2141435635
62
52

Row 2 can be completed with candidates for values 3 and 5. If we try to complete the upper right corner pink piece (to 14) by setting the value for the cell with the question mark, we can find the only possibility for values 3 and 5 on this row and the question mark cell is 1...

421
21414365
62
52

Now consider the greyed block above. There is only one possibility to complete it to 14, and this is using values 6 and 1. This leads to the situation below:

421
21414365
62
34345612


The only possible values to complete the greyed pink block to 14 are 5 and 3. With a 3 on column 2, the location of 4 and 3 in the bottom left block is found. The location of 1 and 4 on row 2 is also easy to find, and the situation is then:

?421
214365
35
6352
345612


The only possible values for the greyed blue cell above are 1 and 6, so the value in the question mark cell must be 3. This allows to complete the entire row 1:

563421
214365
216
3516
6352
345612


At this point, the puzzle can be solved using standard sudoku techniques.