Venture Capital puzzles, solved step by step

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All topicsPower law and portfolio maths10SaaS and unit economics riddles10Probability and expected value10Dilution and ownership riddles9Fund economics riddles8Market sizing and estimation9Growth and compounding8Valuation riddles9Preferences, payouts and protections8Logic and brainteasers6Mental maths and speed tests7Decision and game theory6
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  1. 041Three co-founders own 50%, 30% and 20% of their company. The CTO owns more than the COO. The CEO does not own 30%. The COO does not own the least. Who owns what?Logic and brainteasersWarm upSeed and early-stage VCMulti-stage VC

    Try it first

    Which founder holds 50%?

    Show the worked solution

    The CTO owns 50%, the COO 30% and the CEO 20%. Start with the COO, the person two clues mention. Not owning the least rules out 20. The CTO owning more rules out 50, since nobody can own more than 50. So the COO holds 30, the CTO must hold the 50, and the CEO has the 20 left, which fits the clue that the CEO does not own 30.

    Where should you start a puzzle like this?

    Seating a dinner table works the same way: you begin with the guest who has the most constraints, because each rule about them removes options for everyone else. Start with the person the most clues mention, here the COO, since two clues bear on the COO and each one deletes a column. Not owning the least removes 20. The CTO owning more than the COO removes 50, because there is no larger stake for the CTO to hold. That leaves the COO at 30 before you have used the third clue.

    Elimination grid: cross out, then the last cell standing is the answer50%30%20%CEO555CTO444COO231Order of moves1 COO does not hold the least: not 202 CTO owns more than COO: COO not 503 So COO holds 304 CTO must beat 30: CTO holds 505 CEO gets the 20 left; clue 'not 30' holdsAnswer: CEO 20%, CTO 50%, COO 30%. Only one of the six possible assignments passes all three clues.
    The two clues about the COO cross out 20% and 50%, which fixes the COO at 30%; the CTO must then hold 50% and the CEO 20%, the only one of six possible assignments that passes every clue.

    How do you know the answer is the only one?

    There are only six ways to hand three stakes to three people, so you can check them all, but the grid makes it quicker. Once the COO is fixed at 30, the relational clue forces the CTO into the one stake larger than 30, and the last stake goes to the CEO by elimination. Then use the clue you have not used yet as a check: the CEO holds 20, not 30, so it is satisfied. A clue that was never needed to find the answer but still holds is good evidence you have not made a slip.

    Say the method as you go. An interviewer giving a one-minute logic puzzle is listening for an order of reasoning, not just the answer, so name which clue you use at each step. The trap is to start with the CEO, because the CEO is listed first, and then guess. One clue about the CEO removes only one cell, so you are left trying cases.

    Why would a venture interviewer ask a founders' puzzle?

    It is a warm-up that tests clean reasoning under mild time pressure, dressed in the language of a cap table. It also hints at something real: founder splits rarely follow titles, and an investor reading a cap table should not assume the CEO holds the largest stake. The limitation is obvious: real ownership questions are settled by the share register and the shareholders' agreement, not by inference, and the useful skill here is the elimination habit, not the founders.

    Where candidates lose it

    The common loss is assuming the CEO holds the most and then trying to fit the clues around that. The CEO clue only says what the CEO does not own, and starting there leaves you guessing between two cases.

    The second loss is reading the CTO clue as about the CEO, or forgetting that nobody can own more than 50, which is what rules the COO out of the top stake. Read each clue once, slowly, and cross out the cells it kills.

    What the interviewer asks next

    • If the clue said the CTO owns less than the COO instead, who owns what?
    • Add a fourth founder and a 10% stake. What is the smallest number of clues that can fix every stake?
    • Which single clue could you drop and still get a unique answer?