For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
06/30/2016

Problem 1

You are going to visit your grandmother on Mother's day. You want to give her two cakes. However, to get to her house you must cross seven bridges. At each bridge is a troll who demands Â½ of all of your cakes as the price to pass. However, this troll, being a nice troll, feels bad and gives you back 1 of the cakes that he took.How many cakes must you leave with to be able to give your grandmother 2 cakes?

Problem 2

When Dev was six years old he hammered a nail into his favorite tree to mark his height.

Five years later at age eleven , Dev returned to see how much higher the nail was.

If the tree grew by ten inches each year, how much higher would the nail be?

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Problems from 06/16/16

Problem 1
A cloth bag contains a pool ball, which is known to be a solid ball. A second pool ball is chosen at random in such a way that it is equally likely to be a solid or a stripe ball. The ball is added to the bag, the bag is shaken, and a ball is drawn at random. This ball proves to be a solid. What is the probability that the ball remaining in the bag is also a solid?

Solution:

Problem 2
Suppose N fair 6-sided dice are rolled simultaneously. What is the expected value of the score on the highest valued die?

Solution:

Congratulations to Amit Lele, who was the winner of the last set of puzzles.

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