Took me a minute to even parse what was being asked.
Model the problem as a dynamic programming or greedy problem where tokens move exactly 3 steps right, collect coins on landing, and cannot share positions. Consider the parity of positions and the constraint that tokens cannot overlap, which may require tracking the rightmost token or using a DP state that captures the last occupied position. Aim to maximize coins by deciding which tokens to move and when, possibly using a DP over positions with states representing the number of tokens placed so far.
Pro tip: Clarify the initial configuration and whether tokens can move multiple times; if tokens can move repeatedly, the problem may reduce to selecting a set of non-overlapping landing positions spaced by multiples of 3. Also, consider edge cases like no tokens or no coins.
Restate the rules: tokens move exactly 3 steps right, collect a coin on landing, cannot share a position. Ask clarifying questions about initial setup, number of tokens, and whether tokens can move multiple times.
Note that each move changes a token's position by +3, so the parity of a token's position modulo 3 remains invariant. Also, tokens cannot occupy the same position, so their landing positions must be distinct.
Model as selecting a set of landing positions for tokens such that each is reachable by a sequence of +3 moves from its start, no two tokens land on the same position, and the total coins collected is maximized.
Use dynamic programming over positions, where dp[i] represents the maximum coins collectible considering positions up to i. Transition by either skipping a position or placing a token to land at i if it's a coin and reachable from a start token without conflict.
Discuss time and space complexity (likely O(n) or O(n^2) depending on state). Consider edge cases: no tokens, no coins, tokens already at coins, and overlapping paths.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.