Solving the Merry Christmas Equation

It’s December again and many people are celebrating Christmas. Here in Japan, Christmas is also celebrated even though only less than 1% of the population are Christians.

Anyway, I will be very busy this month, but let’s start our month with solving an equation that will lead to Merry Christmas. Sound confusing? Let’s start.

To understand the solution below, it would help if you have some prior knowledge of about natural logarithms.

The Christmas Equation

Let’s solve the equation y = \displaystyle \frac{ \ln (\frac{x}{m} - sa)}{r^2}  Continue reading

Understanding the Monty Hall Problem

The Monty Hall Problem is one of the famous puzzles that is not very easy to understand.  When Marilyn vos Savant (listed as Highest IQ by Guiness) posted this question in “Ask Marilyn” of Parade magazine, 10,000 readers including 1000 PhD holders wrote to the magazine asserting that Marilyn was wrong despite explanations and mathematical calculations shown. The Monty Hall problem is shown below.

The Monty Hall Problem

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?  Continue reading

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