Optiver·Software Engineer·Technical Phone Screen·Junior

Junior

Jun 2026

Summary

Optiver quant interview, one of those sessions where they hand you a sequence and just stare at you. The math itself wasn't brutal but finding the pattern under pressure with someone watching is a different thing entirely.

Questions Asked (1)

You're given the sequence 1, 3/2, 4, 9½, 23, 55½ and asked to identify the rule generating it, verify that rule holds, and then produce the next two terms.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I stared at the differences first, which was a dead end for a while.

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AI HintsAI Generated

Suggested Approach

First, convert all terms to a common format (e.g., fractions or decimals) to spot patterns. Look for relationships between consecutive terms, such as differences, ratios, or linear combinations. Once a rule is hypothesized, verify it against all given terms, then apply it to find the next two terms.

Pro tip: In trading interviews, it's not just about the answer; it's about demonstrating a systematic, verifiable process. Clearly state your assumptions and show how you test them, as this mirrors debugging and hypothesis testing in software engineering.

1. Normalize the sequence

Convert all terms to a consistent format (e.g., improper fractions or decimals) to simplify pattern recognition. For example, 3/2 becomes 1.5, 9½ becomes 9.5, etc.

2. Explore simple patterns

Check differences, ratios, or alternating patterns. Compute first and second differences, or ratios between consecutive terms, to see if they form a recognizable sequence.

3. Hypothesize a rule

Based on observed patterns, propose a rule that generates each term from previous ones. Consider linear recurrences, polynomial fits, or combinations of arithmetic operations.

4. Verify the rule

Test the hypothesized rule against all given terms to ensure it holds. If it fails, refine or discard the hypothesis and try another pattern.

5. Compute next terms

Once a valid rule is confirmed, apply it to the last term(s) to generate the next two terms in the sequence.

Key Points to Mention

Converting terms to a common format (e.g., fractions) to simplify pattern detection.
Considering both arithmetic and geometric patterns, as well as linear recurrences.
The importance of verifying a rule against all given terms before extrapolating.
Using systematic hypothesis testing, similar to debugging or algorithm design.
Being prepared to explain the reasoning process clearly, as communication is key in interviews.
Acknowledging that multiple rules could fit, but choosing the simplest consistent one.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.