The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three-week long solution process by a pair of ninth-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory as an analytical tool that can explain the course of the exploration towards the insight solution. The explanation is provided by inferring from the data what, how and why the students attended to when working on the problem.