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Comments in green were written by me. Comments in blue were not written by me.
Another great puzzle calendar, thanks!
I eventually coded Day 21 and while I can certainly see how it could be broken down into a very large number of cases for the purposes of calculation, I am wondering if there is an elegant approach to this one?
Blake
on /blog/120
               
@Blake: It's actually not that many different parts. I did it in a spreadsheet, and there were 30 things to calculate. But once I figured out how they should be organized and calculated, each one was very quick.
(anonymous)
on /blog/120
               
@(anonymous): It’s certainly do-able, but whereas I was able to find a single simple summation formula for the day that asked for no odd consecutive amounts, this one has eluded me so just wondering if an elegant approach does exist
Blake
on /blog/120
               
@Blake: there is an elegant solution but it is very different from day 14. If a small hint is allowed:

recurrence relations!
Aisha
on /blog/120
               
@Aisha: Thanks! I did think of that originally but even going back now I can’t seem to find a neat way to apply that approach (and even the OEIS doesn’t seem to give one for the sequence I get solving this for smaller cases). Would be interested to know how you went about this! As it happens, with a bit more thought I did end up finding a single (double-summation) formula that could be used to calculate this
Blake
on /blog/120
               
@Aisha: Hm, I used exactly the same method for both of these days. I'm not sure if it lends itself to a nice clean formula, but it might! I'll share my approach after the contest is over!
Seth Cohen
on /blog/120
               

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