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Jane Street·Data Scientist·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Phone screen for a Data Scientist role at Jane Street. One question, pure mental math and combinatorial reasoning, no calculator allowed. Felt deceptively simple at first glance.

Questions Asked (1)

Q1

You have 5 pumpkins. You weigh every possible pair on a scale, giving you 10 readings: 21, 22, 23, 24, 25, 26, 27, 28, 29, and 30 pounds. You don't know which pair produced which reading. What is the total weight of all five pumpkins?

Algorithms & Data Structures
Author's notes

My first instinct was to try solving for individual weights, which is a dead end without knowing which reading maps to which pair.

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AI HintsAI Generated

Suggested Approach

Recognize that the sum of all 10 pairwise weights equals 4 times the total weight of the 5 pumpkins, because each pumpkin appears in exactly 4 pairs. Sum the given readings and divide by 4 to get the total weight. This avoids needing to determine individual pumpkin weights.

Pro tip: In interviews, look for symmetry and invariants: here, each pumpkin appears in exactly 4 pairs, so the sum of all pairwise weights is a multiple of the total. This shortcut demonstrates strong quantitative reasoning and saves time.

1. Understand the problem

We have 5 pumpkins and all 10 pairwise sums are given but not labeled. We need the total weight of all 5 pumpkins.

2. Identify the key relationship

Each pumpkin is paired with each of the other 4 pumpkins exactly once, so it appears in 4 pairwise sums. Therefore, the sum of all 10 pairwise sums counts each pumpkin's weight 4 times.

3. Compute the sum of the given readings

Add the 10 numbers: 21+22+23+24+25+26+27+28+29+30 = 255.

4. Calculate the total weight

Divide the sum of pairwise sums by 4: 255 / 4 = 63.75 pounds. This is the total weight of all five pumpkins.

5. Verify and conclude

Check that the result is plausible: the average pumpkin weight is about 12.75 pounds, and the pairwise sums range from 21 to 30, which is consistent. State the final answer clearly.

Key Points to Mention

  • Each pumpkin appears in exactly 4 pairs (since there are 5 pumpkins total).
  • The sum of all pairwise weights equals 4 times the total weight of the 5 pumpkins.
  • The sum of the given readings is 255.
  • The total weight is 255 / 4 = 63.75 pounds.
  • This method avoids solving for individual pumpkin weights, which is unnecessary.
  • The approach generalizes: for n items, the sum of all pairwise sums is (n-1) times the total sum.

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