First & Second Setter Notes IP: 184.108.40.206 Posted on January 17, 2017 at 01:59:41 PM by MatriX
First of all a big thank you for all the kind comments on The First & The Second. As a couple of you surmised a gremlin had somehow got into the works which resulted in a more difficult puzzle than was intended. This meant there were 3 slightly different solutions instead of the intended single solution to the first part, so a big apology for that. Fortunately, this ambiguity was resolved by the second part of the puzzle which necessitated the sum of the puzzle digits to be divisible by 11.
Some of you wondered how the puzzle was constructed. It was the idea of the first Noel = no L and the fact that there was an L pentomino that prompted the approach. Removing that pentomino leaves 11 remaining pentominos requiring 55 squares determining the unique 5x11 rectangular grid. Having found a suitable pentomino configuration to fill the grid I then labelled the five squares in each pentomino shape with the digits 1 to 5, attempting while doing so to avoid creating alternative 1 to 5 configurations.
After a final check that the resultant numbering did indeed give a unique fill, I increased two of the elements labelled 2 to 5 in each pentomino by 4. The total of the five digits thus increased from 15 to 23 but without affecting the uniqueness of the pentomino layout. This brought the full range of digits 1 to 9 into play and helped mask the underlying pentomino involvement. Also, the absence of zeros meant that wherever I inserted bars in the grid there would be no ineligible zero starts. I began by inserting bars wherever things looked promising e.g. 15dn&21ac both squares. Finally, where it could be done safely, I tweaked a few of the pentomino numberings to reintroduce zeros safely into the puzzle to make the whole thing look more natural.
Despite the smoke screen some solvers had twigged the Noel early on, so clearly I had not been devious enough!