Brain Teasers & Word Problems

1. Suppose you have ten bags of marbles with ten marbles in each bag. If one bag weighs differentlyn the other bags, and you could only perform a single weighing, how would you figure out which one is different?

 2. You are about to hop on a plane to Seattle and want to know if you should carry an umbrella. You call three friends of yours that live in Seattle and ask each, independently, if it’s raining.

 3. Each of your friends will tell you the truth ⅔ of the time and mess with you by lying ⅓ of the time. If all three friends answer “Yes, it’s raining,” what is the probability that is it actually raining in Seattle?

 4. Imagine you are working with a hospital. Patients arrive at the hospital in a Poisson     Distribution, and the doctors attend to the patients in a Uniform Distribution. Write a function or code block that outputs the patient’s average wait time and a total number of patients that are attended to by doctors on a random day.

 5. Imagine there are three ants in each corner of an equilateral triangle, and each ant randomly picks a direction and starts traversing the edge of the triangle. What’s the probability that none of the ants collide? What about if there are N ants sitting in N     corners of an equilateral polygon?

 6. How many trailing zeros are in 100 factorial (i.e. 100!)?

 7. Imagine you’re climbing a staircase that contains n stairs, and you can take any number k steps. How many distinct ways can you reach the top of the staircase? (This is a modification of the original stair step problem)

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