Digits 1-9 with *+ Count

This combinatorics question is about counting how many different arithmetic expressions can be built by placing operators, or nothing, between a fixed sequence of digits while keeping their order. It lives at the intersection of basic discrete math and the kind of symbolic reasoning that often appears in quantitative finance interviews and quant prep material. Because there is no reordering, all the structure comes from the pattern of insertions.

It trains recognition of independent choice points, abstraction of a concrete symbolic setup into a counting framework, and disciplined enumeration without overcounting. It also reinforces comfort with combinatorial reasoning on strings, something that recurs in more advanced probability and algorithm questions in quant interviews.

This matters for quant interviews because it checks whether you can quickly turn a worded puzzle into a clean combinatorial model, argue correctness, and reason systematically under time pressure.

What it tests

This problem class is governed by the multiplication principle of combinatorics, which states that when a process involves a sequence of independent choices, the total number of possible outcomes is the product of the number of options at each stage. In problems where you have a string of objects (like digits or letters) and must decide what to insert between them, each gap represents an independent decision point. The total number of distinct configurations is the product of the number of choices available at each gap. This principle holds because the choice made at one gap does not constrain or affect the choices at the others, so all combinations are possible. The essence is recognizing independence and mapping the problem to a sequence of such choices.