Time Required for Snail to Reach Food

This brain teaser is about repeated progress that is partially undone at regular intervals. It belongs to a family of quant interview questions where motion or accumulation is opposed by some kind of reset or erosion. The twist is that the situation changes qualitatively as you get closer to the goal, so you must reason carefully about when the pattern stops instead of blindly extending it.

It trains your sense for net change, discrete-time thinking, and careful interpretation of stopping conditions. Solving it cleanly reinforces your intuition for processes with alternating gains and losses, a core idea behind many quant prep exercises on this platform. It also sharpens attention to wording and timing.

For quant interviews, this matters because market PnL, inventory, and risk often evolve in steps, with frictions that partially offset gains. Interviewers want to see you model such dynamics logically and precisely.

What it tests

Problems involving alternating progress and setbacks, like forward movement and backward drift, are governed by the idea of net gain per cycle. The key is to recognize that each cycle (here, an hour) consists of a predictable advance and retreat, so the effective progress is the difference between the two. However, the structure changes when the goal is within reach: if the forward movement in a cycle is enough to reach or surpass the target before the setback occurs, the process ends immediately upon arrival. This principle holds because the system is discrete and the 'reset' (here, the wind gust) only happens at the end of each cycle, not continuously.