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    $\begingroup$ Cool! But "We want to find the value of the larger number" (a quotation from the question) — not merely who picked it. Can you edit to explain how we know that'll be done within the requisite number of turns? $\endgroup$
    – msh210
    Commented Jul 18, 2023 at 4:40
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    $\begingroup$ A binary search will take up to 999 questions for one person, but you could need twice that if Bob and Charlie's numbers are close together. $\endgroup$
    – fljx
    Commented Jul 18, 2023 at 7:40
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    $\begingroup$ To put the other comments in plain English: there are (several) cases where this approach hits the question limit without finding the larger number, and thus fails the given task. Also, it will often hit the question limit without finding even the person with the larger number. To condense even further: "This doesn't work. At all." $\endgroup$
    – Bass
    Commented Jul 19, 2023 at 16:07
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    $\begingroup$ Not to mention a 300-digit number can only range from $10^{299}$ to $10^{300}-1$, not $10^{300}$ to $10^{301}-1$. $\endgroup$
    – Nautilus
    Commented Jul 20, 2023 at 13:47
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    $\begingroup$ @Nautilus according to OP's comment on my comment, leading zeros are allowed. So, the range is from $0$ to $10^{300}-1$. $\endgroup$
    – theozh
    Commented Jul 21, 2023 at 13:57