After giving up, the lingering question was "how well could we have done, given more time to devise an accurate method for predicting the number of halos?" Neither of us are big fans of unanswered questions, so we took a semi-sketchy approach to answering this question...
The competition's best benchmark predictions were produced by the existing LENSTOOL software, and those predictions were available to all participants. We had noticed early on that in these predictions, skies 1-40 each have one halo, skies 41-80 each have two halos, and skies each 81-120 each have three halos. We used this information and our position method to determine the positions of these known quantities of halos.
This last try achieved a score of 1.08476. It did not beat the LENSTOOL method (our original goal), but it was damn close. How well could we have done with more time to devise an accurate method for predicting the number of halos? Pretty well, in our humble opinion.
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