Google·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Google interview with a geometry/math puzzle that turned into a surprisingly deep design discussion. The question sounds like a brain teaser but they really wanted to see how you reason through tradeoffs and generalize solutions.

Questions Asked (1)

Given a square, divide it into N regions of equal area. Walk through multiple approaches, discuss constraints on cut shapes, and explain how your strategy handles arbitrary values of N including odd ones.

Algorithms & Data StructuresTechnical Trade-offsAdaptability & Ambiguity

Author's notes

I started with parallel slices because that felt obvious, N vertical cuts, done.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and constraints, then present multiple approaches ranging from simple to complex, discussing trade-offs and how each handles arbitrary N. Emphasize a general strategy that works for any N, including odd values, and explain the reasoning behind your choices.

Pro tip: Demonstrate adaptability by first proposing a simple solution, then iterating to handle edge cases and constraints, showing you can think on your feet and consider trade-offs like cut complexity and feasibility.

1. Clarify the problem

Ask questions to understand constraints: Are cuts required to be straight? Can regions be non-contiguous? What is the definition of 'region'? This shows you consider ambiguity and scope.

2. Propose simple approaches

Start with straightforward methods: for even N, divide into N/2 horizontal strips and split each; for odd N, use a combination of strips and a central region, or use a grid when N is composite.

3. Generalize for arbitrary N

Introduce a universal method: use a spiral cut or a recursive subdivision that works for any N, explaining how it ensures equal area and handles odd N.

4. Discuss constraints and trade-offs

Compare approaches based on cut complexity, number of cuts, shape regularity, and feasibility. Mention that some methods may require curved cuts or many pieces.

5. Conclude with a recommended strategy

Summarize the best approach for the given context, justifying why it balances simplicity, generality, and practicality.

Key Points to Mention

Equal area division methods: horizontal strips, grid, spiral, recursive subdivision
Handling odd N: combining even division with a central region or using a spiral that naturally accommodates any N
Constraints on cut shapes: straight vs. curved cuts, number of cuts, and whether regions must be connected
Trade-offs: simplicity vs. generality, number of cuts vs. shape regularity
Mathematical reasoning: area preservation, geometric construction, and proof of equal area
Adaptability: how to modify approach if constraints change (e.g., only straight cuts allowed)

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