In the grid below, the X-cells should not be filled, and they mark the separation of the numbers in the rows and in the columns. All the others cells should be filled with a digit from 1-9. The numbers that appears above the first row, indicates the sum of the digits in the "blocks" of cells of the corresponding column, and similarly, the numbers at the left of the first column, indicates the sum of the digits in the "blocks" of the corresponding row. That is, in the first row (with three "blocks" of numbers), the digits of the first "block" must add to 11, those of the second "block" must add to 7, and those of the third "block" must add to 13. In the first column, there are two "blocks" of numbers, and the digits of the first must add to 23 and those of the second must add to 20, etc...

             23  11  17  10  32   6  11   4  21  14  16
             28  15      16   8  16  15  13  11  22   5
                         14              10 
            +---+---+---+---+---+---+---+---+---+---+---+
11/07/13    |   |   | X |   |   | X |   |   |   | X | X |
            +---+---+---+---+---+---+---+---+---+---+---+
16/16/10    |   |   | X |   |   | X |   |   |   |   | X |
            +---+---+---+---+---+---+---+---+---+---+---+
10/22/16    |   |   |   | X |   |   |   | X |   |   |   |
            +---+---+---+---+---+---+---+---+---+---+---+
14/17       | X | X |   |   |   |   | X | X | X |   |   |
            +---+---+---+---+---+---+---+---+---+---+---+
29/10       | X |   |   |   |   | X |   |   |   |   | X |
            +---+---+---+---+---+---+---+---+---+---+---+
07/22       |   |   |   | X | X | X |   |   |   | X | X |
            +---+---+---+---+---+---+---+---+---+---+---+
14/08/10    |   |   |   |   | X |   |   | X |   |   | X |
            +---+---+---+---+---+---+---+---+---+---+---+
08/19/06    |   |   | X |   |   |   |   |   | X |   |   |
            +---+---+---+---+---+---+---+---+---+---+---+
13/14/13/13 |   |   | X |   |   | X |   |   | X |   |   |
            +---+---+---+---+---+---+---+---+---+---+---+

No "block" has repeated digits. Fill this grid.

(In reply to NOT ONE, BUT TWO TYPOS. by pcbouhid)

I think there may be another typo you missed.  It's still impossible.

I started solving it, until I found a square that could contain no number.  I started over from the beginning in hopes of finding the contradiction's location.  Here it is:

             23  11  17  10  32   6  11   4  21  14  16
             28  15      16   8  16  15  13  11  22   5
                         14              10 
            +---+---+---+---+---+---+---+---+---+---+---+
11/07/13    |   |   | X |   |   | X |   |   |   | X | X |
            +---+---+---+---+---+---+---+---+---+---+---+
16/16/10    |   |   | X |   |   | X |   |   |   |   | X |
            +---+---+---+---+---+---+---+---+---+---+---+
10/22/16    |   |   |   | X |   |   |   | X |   |   |   |
            +---+---+---+---+---+---+---+---+---+---+---+
14/17       | X | X |   |   |   |   | X | X | X |   |   |
            +---+---+---+---+---+---+---+---+---+---+---+
29/10       | X |   |   |   |   | X |   |   |   |   | X |
            +---+---+---+---+---+---+---+---+---+---+---+
07/22       |   |   |   | X | X | X | 5 |   | ? | X | X |
            +---+---+---+---+---+---+---+---+---+---+---+
14/08/10    |   |   |   |   | X |   |   | X | 4 | 6 | X |
            +---+---+---+---+---+---+---+---+---+---+---+
08/19/06    |   |   | X |   |   |   |   |   | X | 5 | 1 |
            +---+---+---+---+---+---+---+---+---+---+---+
13/14/13/13 |   |   | X |   |   | X |   |   | X | 9 | 4 |
            +---+---+---+---+---+---+---+---+---+---+---+

According to the horizontal sum, the ? must be a 9 or 8.  According to the vertical sum, it must be 6 or less.

Edit:  We all make mistakes.  There's a math mistake in this comment.  PCB is correct, then.

Edited on January 13, 2006, 11:31 am

Posted by Tristan on 2006-01-12 21:02:25