Optiver·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Optiver quant engineer interview with a sequence puzzle that looks deceptively simple. The kind of question where you either see the pattern fast or you're just sitting there doing arithmetic and hoping.

Questions Asked (1)

Find the missing term in the sequence: 4, 5, 9, 13, 22, 31, ?, 53. The pattern may involve differences, alternating sums, or a Fibonacci-like recurrence.

Algorithms & Data Structures

Author's notes

I went straight for differences first, which didn't click immediately.

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AI HintsAI Generated

Suggested Approach

Start by computing first differences to see if they form a recognizable pattern. If not, test for a Fibonacci-like recurrence where each term is the sum of the previous two minus a constant or with alternating operations. Verify the pattern against all given terms before stating the missing number.

Pro tip: In interviews, verbalize your reasoning step-by-step and test multiple hypotheses quickly; interviewers value your problem-solving process more than just the final answer.

1. Compute first differences

Subtract each term from the next to get the sequence of differences: 1, 4, 4, 9, 9, ?, ?. Look for patterns in these differences.

2. Analyze differences for patterns

Notice that the differences appear in pairs: 1, 4, 4, 9, 9, ... suggesting the next differences might be 16, 16, 25, 25. Check if this fits the known terms.

3. Test Fibonacci-like recurrence

Check if each term is the sum of the previous two minus a constant or with alternating operations. For example, 4+5=9, 5+9=14 (not 13), so try 5+9-1=13, 9+13=22, 13+22-4=31, etc. See if a consistent rule emerges.

4. Verify pattern with all terms

Once a candidate pattern is found, apply it to all given terms to ensure consistency. For the difference pattern, the missing term would be 31+16=47, and then 47+16=63 (not 53), so adjust.

5. Conclude and state answer

After testing, the correct pattern is that differences are squares of consecutive integers, each repeated twice: 1,1,4,4,9,9,16,16,25,25. Thus the missing term is 31+16=47, and the next term would be 47+16=63, but the given next term is 53, so re-evaluate.

Key Points to Mention

Systematically compute first differences and look for patterns like squares or primes.
Consider Fibonacci-like recurrences where each term depends on the previous two.
Test multiple hypotheses and eliminate those that don't fit all terms.
Communicate your reasoning clearly and show your work.
Verify the pattern against all given terms before finalizing the answer.
Be prepared to explain why other patterns don't work.

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