Beat the Taxman with 1-10 Numbers

This brain teaser is about navigating a web of divisibility constraints inside a tiny, fixed universe. Each choice reshapes the board by wiping out related values through divisor links, so the entire quant prep challenge is understanding how local moves restrict or enable future high-value picks. It compresses number theory, game structure, and foresight into a very small, discrete setting ideal for timed interviews.

It trains your ability to see hidden graph-like structure in plain arithmetic, to reason about cascading constraints, and to plan multi-step sequences under irreversible choices. You practise evaluating trade-offs between immediate gain and future optionality, as well as quickly scanning for patterns in divisor relationships.

This matters for quant interviews because trading, risk, and algorithmic decisions often resemble this: every action kills or creates future paths. Interviewers use such questions to test strategic thinking, combinatorial intuition, and disciplined optimization under constraints.

What it tests

This problem class is governed by the structure of divisor relationships within a set of integers and the way choices cascade through these relationships. Whenever you claim a number, you also remove all its divisors from the pool, which can block you from claiming other numbers that share those divisors. The optimal strategy is to maximize your sum by prioritizing numbers whose divisors are minimally shared with other large numbers, especially focusing on numbers with large, unique divisors (often the largest primes or numbers with few divisors left). The principle is to sequence your picks to claim the largest available numbers while minimizing the collateral loss of potential future picks, which is dictated by the web of divisibility among the numbers. This structure holds because the removal of divisors is irreversible and can preclude access to high-value numbers if not planned carefully.