A simply worded riddle this week on The Riddler, about four ropes having non-uniform and unknown burning rates, the only constraint being they all burn completely in one hour. With the help of a lighter (or even a single match), what are the possible units of time one can measure by burning them?
While I had worked out a range of possible times for each of the ropes to complete its combustion, I went for a simulation based confirmation. The starting point is that a new fire can only be started when a burning rope ends up burning. Which only happens for a finite number of possibilities. I found 24 of them, consisting of
> total*prec  0.000 0.5000 0.750 0.875 0.9375 1.000 1.125 1.1875 1.25 1.3125  1.375 1.4375 1.500 1.625 1.7500 1.875 2.000 2.1250 2.25 2.5000  2.750 3.0000 3.500 4.000
i.e., some combinations of 1, 2⁻¹, …, 2⁻⁴, with the comment that those times cannot all be obtained within a single arson experiment.