# Visualizing One Million vs. One Billion

From the YouTube description: “There are lots of ways to compare a million to a billion, but most of them use volume. And I think that’s a mistake, because volume just isn’t something the human brain is great at. So instead, here’s the difference between a million and a billion, in a more one-dimensional way: distance.

The video is more than an hour long, which is the point. In the last minute of the video, he mentions what a trillion would be in the same scenario.

# Another Poorly Written Word Problem: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series poorly written word problem, taken directly from textbooks and other materials from textbook publishers.

Part 2: Estimation and rounding.

Part 3: Probability.

Part 4: Subtraction and estimation.

Part 5: Algebra and inequality.

Part 6: Domain and range of a function.

Part 7: Algebra and inequality.

Part 8: Algebra and inequality.

Part 9: Geometric series.

Part 10: Currently infeasible track and field problem.

Part 11: Another currently infeasible track and field problem.

# 211

Set a digital clock to display in 24-hour (military) time. Each day, it will show you 211 prime numbers starting with 00:02 (2 minutes after midnight) and ending with 23:57 (3 minutes before the next midnight.)

Oh, and 211 is also prime, so 02:11 would be one of the 211 prime times you observe each day.

# Incredibly difficult math puzzle

For math/puzzle enthusiasts (as well for as my own future reference): This was one of the most diabolically difficult puzzles that I’ve ever seen. The object: use the numbers 1-9 exactly once in each row and column while ensuring that the given arithmetical operation in each cage is also correct. Here it is. Fair warning: while most MathDoku+ puzzles take me 20-40 minutes to solve, this one took me over 3 hours (spread out over 5 days).

# Repunit prime

In the United States, today is abbreviated 10/31. Define the $n$th repunit number as

$R_n = \frac{10^n-1}{9} = 1111\dots1$,

a base-10 number consisting of $n$ consecutive 1s. For example,

$R_1 = 1$

$R_2 = 11$

$R_3 = 111$

$R_4 = 1,111$,

and so on.

It turns out that $R_{1031}$ is the largest known prime repunit number.

# Pizza Hut Pi Day Challenge: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on the 2016 Pizza Hut Pi Day Challenge.

Part 1: Statement of the problem.

Part 2: Using the divisibility rules for 1, 5, 9, 10 to reduce the number of possibilities from 3,628,800 to 40,320.

Part 3: Using the divisibility rule for 2 to reduce the number of possibilities to 576.

Part 4: Using the divisibility rule for 3 to reduce the number of possibilities to 192.

Part 5: Using the divisibility rule for 4 to reduce the number of possibilities to 96.

Part 6: Using the divisibility rule for 8 to reduce the number of possibilities to 24.

Part 7: Reusing the divisibility rule for 3 to reduce the number of possibilities to 10.

Part 8: Dividing by 7 to find the answer.