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5 pirates of different ages have a treasure of 100 gold coins. On their ship, they decide to split the coins using this scheme: The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it. If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard. Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?
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Trader

Interviewed at Jane Street

4.4★
Jul 17, 2013

5 pirates of different ages have a treasure of 100 gold coins. On their ship, they decide to split the coins using this scheme: The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it. If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard. Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?

There exists a six-sided die. The die is rolled. You are paid $x if the die shows x dots (e.g. if you roll 3, then you are paid $3). What is a fair price for this game? Additional layer: after rolling the die once, you have the option of taking the rolled amount or rolling again. However, if you roll again, then you must take the amount corresponding to the second roll. What is a fair price for this game?
avatar

Assistant Trader

Interviewed at Jane Street

4.4★
Mar 9, 2010

There exists a six-sided die. The die is rolled. You are paid $x if the die shows x dots (e.g. if you roll 3, then you are paid $3). What is a fair price for this game? Additional layer: after rolling the die once, you have the option of taking the rolled amount or rolling again. However, if you roll again, then you must take the amount corresponding to the second roll. What is a fair price for this game?

Find the largest 5-digit number such that the pairwise digit sums of the numbers are unique. Find the smallest 5-digit number with the same property. Explain why it doesn't work for 7-digit numbers. Does it work for 6-digit numbers?
avatar

Trader

Interviewed at Optiver

3.7★
Oct 4, 2016

Find the largest 5-digit number such that the pairwise digit sums of the numbers are unique. Find the smallest 5-digit number with the same property. Explain why it doesn't work for 7-digit numbers. Does it work for 6-digit numbers?

You have 3 cards, each labeled n, n+1, n+2 and you don't know n. The rules of the game: All cards start face down. You flip one card. If you "stay", you get that card's value. If you don't "stay", then you flip another card. Again, choose to "stay" (and keep the 2nd card's value) or flip the final card and keep the final card's value. Design the optimal strategy.
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Trader Internship

Interviewed at Optiver

3.7★
Jan 4, 2017

You have 3 cards, each labeled n, n+1, n+2 and you don't know n. The rules of the game: All cards start face down. You flip one card. If you "stay", you get that card's value. If you don't "stay", then you flip another card. Again, choose to "stay" (and keep the 2nd card's value) or flip the final card and keep the final card's value. Design the optimal strategy.

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