Leaked interview questions from a finance company

[ru_linux_geek]

I don't know which company these are from. It's funny how I'd be pissed if my interview questions leaked, but here I am leaking questions. I think #1 is particularly interesting, but that is just maybe because it confounded some of my coworkers.

1. Redacted


2. The following decision procedure is used to pick a red or black ball from a pair of jars.

Comments

[certron]

The second one is easy: put the black marbles in the jar first. :-)

[technoviking]

The set of initial position and velocity (p,v) is countable. Given a mapping f from Z+ to ZxZ, at time t>0 bomb p+v*t.

For the second problem, place 1 red marble in one jar, the remaining marbles in the other jar. This can be shown to be a maximum probability as follows. Let r,b be the number of marbles in the 1st jar. WLOG p(red) for the 1st jar >= 1/2, p(red) for the 2nd jar <= 1/2. If the first jar has at least one blue marble, p(red) is at most 50/51, and p(red) for the 2nd jar is at most 1/2. The scenario posited to be best has this sum equal to 1+49/99 = 148/99. The other case has sum at most 50/51 + 1/2 = 151/102. Now 148/99 > 3/3, so by the intermediate property of fractions, 148/99 > (148+3)/(99+3) = 151/102.

[anonymous]

I got #1 as a google interview question.

3 would be that everyone comes outside and stands in the middle where the red hats and black hats meet

[anonymous]

That was me. I am Marla.

[ru_linux_geek]

Did you ever figure out the random set of points that needs to meet somewhere problem?

[ru_linux_geek]

Thanks, I'll at least not leak the question anymore.