Pappacom - The 2 puzzles with multiple solutions

were Pappacom puzzles from T2 in The Times a few weeks ago. This was before either the Telegraph or the Daily Mail started doing them. Therefore, they must have been Pappacom.

I elected to guess one of 2 possible numbers that I thought might unlock things. Having tried one guess successfully, I then thought I'd try the other. To my surprise, I came up with another valid solution. Knowing more now about the finer logical tricks one can use, I accept that I can now always solve these puzzles without resorting to guesswork.

I photocopy the puzzle so that (a) I can erase if necessary without ripping T2 and (b) I can start again if I really stuff it up. Transcription errors are not the issue. These puzzles occured before I designed the spreadsheet.

When I do transfer the puzzle to the spreadsheet (if I haven't managed to solve it in my coffee breaks at work) I transcribe row by row, then check once column by column, then re-check box by box. Again, transcription errors are not the issue.

IJ - Please go back and read my posts again. This is twice now that I've said that my spreadsheet has conditional formatting on the row, column and box summation cells. This turns the summation cell green IF AND ONLY IF THERE IS ONE OF EACH DIGIT in the associated row, column or box. If there are any duplicates, it doesn't turn green no matter whether it adds up to 45 or not. I appreciate the time you took making up that 4 x 4 grid to illustrate your point, but I had that possible error covered, as I stated a few posts earlier (This thread, post date - Fri Mar 11, 2005 8:21 pm). That is now the third time I've explained my logic in one thread.

For a copy of my spreadsheet,

Click Here. The only cells that are unlocked are those for game entries, so I don't end up trashing my formulae by clicking in the wrong cell by mistake. There is no password on the spreadsheet, so it is a simple matter to unprotect it and see the formulae for yourself. To see the conditional formatting, highlight one of the summation cells then click on "Format" on the main menu bar, then "Conditional Formatting". Each one uses an AND statement with 9 COUNTIF conditions, one for each digit 1 - 9 in the row/column/box to which it refers. The end result of each AND statement will only be "TRUE" if

all of its COUNTIF conditions are "TRUE" and it will then turn the cell green. If there are any duplicates, then one of the COUNTIF conditions will be "FALSE" and thus the AND statement will return a "FALSE" result, which means the cell stays white. When all 27 summation cells are green, the puzzle is solved. QED.

When you've finished looking at how I've prorammed the spreadsheet, close Excel

without saving changes. It is very easy to mess up the conditional formatting statements if you try to use the arrow keys to see what's going on (use the mouse instead - click, hold and drag to scroll the statement in the little window). If you find that the cells don't turn green with a valid solution, then you stuffed up the formatting, so you need to download it again.