Thoughts on Puzzle 19 : Wild Thermometers

Ok, you can start with the rows and columns with the smallest sum of filled spaces, which is 1 in this case.
Observe the row with 1 on the left, there are three thermometers in that row which has more than 1 space within that same row. Those are (delta), (gamma) and (epsilon), and only the bulb part of those thermometers can possibly be filled. So you can mark the remaining parts of those three thermometers as red or ‘0’. This way you remove the cells which will never be filled.
Similarly do the same for the column with 1 on the top, you can see towards the bottom of that column, only one thermometer (gamma) that came from a nearby column and it has more than 1 cell within that column. You can mark the tail part of that thermometer as red or ‘0’.

Do the same for the rows with 3 as the sum.

Mark green or ‘1’ where you know a cell of a thermometer will definitely be filled. And hence, starting from that point to the bulb will definitely be filled.

Then the cells where a thermometer has bent are also crucial. By using the above strategy, you can determine which part of a bent thermometer will be filled or unfilled.

This way, gradually you will progress towards the solution.

I solved this with LPSolve IDE which is an open source program for solving integer linear programming problems.
lp_solve reference guide (5.5.2.11) (sourceforge.net)

I followed this same algorithm as well. But in order to make an easy tool to find places to target, I created a scoring system by multplying the column and row number and the last dimension was the distance from the bulb. The bulb was a value of 7, the next square in a thermometer was a 6 and so on.
The scoring system wasn’t truly deterministic, but it created a colored heatmap of where I should apply my rules for ruling specific square in or out.

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I had a bit of trouble with it at the beginning until I threw it in photoshop and used it to clean up my work and figured a clean way to mark trial and error. Once I had that and marked off any spaces that couldn’t be it, I found a lot of information through trying out every solution for one of the rows that only had 1 space. It went pretty quick from there.