Puzzle Description:

A pumpkin waiting to be lit up for Halloween.

#1: Jane Doe (telly) on Oct 28, 2008

Have a great 31st! :)

hard one - but great to have another puzzle that requires no guessing - very nice.

Here's how I did this one:

Eyes/nose/top-edge-of-mouth region can all be worked out by careful color logic. Once you've done that, you have a bunch of black 1's for the bottom of the mouth, which can be done with the fancy smile logic (see example 9 in the advanced puzzle solving techniques tutorial). I then looked at the red fours in row three and was able to see that a contradiction follows if either one was touching the outer edge of the puzzle.

At this point the red 14's on the sides were almost completely placed. They had 13 cells filled in and one cell that could be either at the top or the bottom. The three bottom rows had 4 red cells already painted and adding up the clue numbers for those three rows, I saw that 20 more were needed. But looking at the column clues for the center 18 columns, I had only 18 red cells to fill in on the bottom part of the puzzle. To get the 20 red cells I needed to complete the bottom of the puzzle, the only possibility was that the missing reds in the two edge columns were at the bottom, not the top. With those filled in the whole bottom of the puzzle solved.

(This is the first time I've used that kind of amortization argument in solving a puzzle - if the row or column clues can let you count up how many cells need to be colored in a region, then you can draw some conclusions about how things in the other direction need to be arranged to get that many cells into the region. I don't know if that might be more frequently possible or not.)

Three more applications of smile logic along the top edge finished things up.

So this puzzle, by accident or design, turns out to be very interesting and challenging to solve logically. Very cool. Thanks.

Actually, I'm not sure the term "amortization argument" is used in the way I used it in the previous post by anyone except computer scientists analyzing algorithms. I should call it something else.

Though this is the first time I actually used that counting trick, I think it might be more generally useful, so I added it to the "Advanced Puzzle Solving Techniques" page. I called it "Summing".

Mostly color solving for me but I used what I call extended smile logic in a couple places and it all work out.

Creepy clown-kitty-face pumpkin.

I kept thinking it was a decorated apple. Cute and fun!

Goto next topic

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