Measuring 45s with Two Fuses

This brain teaser asks you to time a specific sub-minute interval using only two combustible fuses and a single way to ignite them, under the constraint that the fuses burn at irregular rates along their lengths. Each fuse has a known total burn time but no local uniformity, so you cannot simply mark off fractions by length. The challenge is to design a sequence of lightings that guarantees a precise duration, even though you can never rely on how fast any given segment will burn. Variants of this style of puzzle occasionally appear in logic-centric interviews and quantitative reasoning screens.

Solving it leans heavily on recognizing invariants and exploiting relative rather than absolute rates. The key conceptual step is understanding how lighting an object from multiple points changes the total completion time in a way that is independent of local irregularities. Interviewers watch for whether a candidate can abstract away from the messy details, reason cleanly about processes running in parallel, and construct a step-by-step strategy that provably yields the target time interval.

What it tests

This problem class is governed by the principle of exploiting invariants and relative rates in systems where absolute rates are unknown but total duration is fixed. When an object (like a fuse) burns unevenly but always takes the same total time to burn, lighting it from both ends guarantees it will finish in half the time, regardless of local speed variations. This is because the two flames approach each other, each consuming whatever portion of the fuse is in front of them, so together they traverse the entire length in half the time. The key is that the total burn time is invariant, and splitting the process spatially (lighting both ends) splits the time evenly, even if the path is not uniform.