go forth and X [or the reverse]

The New Year Riddle is about optimisation: starting with a single machine, between delivering one unit per machine – hour and delivering one new machine per machine every six days, what is the maximal number of units produced over 100 days?

Comparing the amounts produced by k machines after 6log₂(k) days used to multiply the machines showed that 2¹⁵ -1 additional machines were first produced, to generate 7864320 items over the remaining 10 days. Which did not really require an R implementation (although I checked that intermediate solutions where only some of the machines were producing new machines were sub-optimal).