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TL;DR

Invariant Arguments: The Parity Trick: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Jane Street, SIG, Optiver, IMC, Citadel.

By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateClever Arguments

Invariant Arguments: The Parity Trick

Asked at: Jane Street, SIG, Optiver, IMC, Citadel

Problem
On a board, the numbers 1,2,3,,251, 2, 3, \ldots, 25 are written. In each move, you pick any two numbers aa and bb, erase them, and write ab|a - b| in their place. After 24 moves, one number remains. (a) Can the final number be 0? (b) Can the final number be 1? (c) What are all possible final numbers?
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