Wall Street Brainteasers/Puzzles

Interview process/preparation
#1

Some hedge funds, trading firms and investment banks love to ask their markets candidates crazy/far-fetched brainteasers and probability questions sometimes, make them swear a bit :grinning_face_with_smiling_eyes:. So we are starting a Meet here with series of questions compiled over the years from real interviews. let me know if you want answers to any!

  1. The probability to see a falling star in the sky over the course of one hour is 0.64. What is the probability to see it over the course of half an hour?

  2. You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

  3. Using only a 4 minute and 7 minute hourglass or egg timer how would you measure exactly 9 minutes?

  4. You have 25 horses, you want to pick the fastest 3 horses out of those 25. In each race, only 5 horses can run at the same time. What is the minimum number of races required to find the 3 fastest horses without using a stopwatch?

  5. We are to play a version of Russian Roulette, the revolver is a standard six shooter but I will put two bullets in the gun in consecutive chambers. I spin the chambers, put the gun to my head pull the trigger and survive. I hand you the gun and give you a choice…
    You may put the gun straight to your head and pull the trigger, or you may re-spin the gun before you do the same. What is your choice and why? How does this differ from the case with only one bullet?

  6. How many degrees (if any) are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?

  7. What is the expected number of times a fair die must be thrown until all scores appear at least once?

  8. Watermelon is 99% water. I have 100 pounds of watermelon. After a week, drying in the sun, the shriveled watermelon had only dried down to being 98% water. What is the total weight of the watermelon now?

  9. what’s 16 cubed?

  10. A 4x4x4 cube is made of 1x1x1 cubes. If I paint the outside, how many 1x1x1 cubes have paint on them?

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#2

  1. An hour is two half hours. If the probability in each half hour is p, the probability not to see a falling star in the entire hour is (1−p)*2=1−0.64=0.36, so 1−p=0.6 and so p=0.4.

  2. burn one string from both ends, which will take 30mins. At the same time, burn the other string from one end. Once the first string has burned completely, burn the second string at other end as well. It will take 15 mins (in additional to first 30 mins), so 45mins total, for second string to completely burn.

#3

can someone help answer 4?

#4

This is great! but would you mind also posting some questions for SWE interviews? ty

#5

basically starting by numbering your horses and dividing then into groups of 5: 1-5, 6-10, 11-15, 16-20, 21-25. 5 races will gives us the order within each group. assume that it’s same number order within each group with loss of generality, ie 1,6,11,16,21 are the fast within each group, and you can safely ignore the last 2 horses from each group.

then we race 1,6,11,16,21, and assume order is same number order, ie 1 is the fastest, therefore we can eliminate 4-5, 8-10, 12-15, 16-20 and 21-25. our last race includes 2,3,6,7,11, and we have top 3 with 7 races in total.

#6

Hi, sorry if this is a bit too late. But you can check the following link

LeetCode is the standard preparation interview platform for SWE in both Tech and Finance. I have always found any question I was asked for in interviews there, with the solutions, no need to have a premium account, just check the discussions, you will always find a benefactor sharing a solution (more than one usually). Best of luck.