quantitative trader interview questions shared by candidates
Round 2: If you have balls weighting from 1, 2, ... 40g, and you have a fair balance, how many of their weights you have to know in advance such that you can measure all the rest?
If you can weigh 1,...,n-1 for n > 2, then you can weigh n by using 1 and n-1 (this does not hold for weighing 2). So you just need 1 and 2.
Not sure I fully follow the question, can't you just get everything in terms of the lightest, so just weigh the lightest to get your unit? e.g. number the weights w1, w2, ... ,w40 in increasing order (we can determine this without external knowledge, right?). Then we have w1 + w2 = w3 w1 + w3 = w4 w1 + w4 = w5 and also stuff like w2 + w3 = w5 substitute come stuff in and you find that w2 = 2w1, hence wn = nw1 So just 1?
I play a game where I start with a score of 100. I then flip 10 coins in a row. Every time I get a head I add 1 to my score. When I get a tails I take the reciprocal of my score. If you are running this game, and people are given their score in pounds at the end of the game, how much would you charge people to play?
Google the game 'Shut the box'. He asked me to figure out the average score someone has at the end of the game if they play the 'optimal' strategy. After getting this number, he wanted to know how this would change if instead of playing the optimal strat, they made random moves. Super open ended problem.
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