Fallout 4 Math, Part 2

This post is the second part in a series. If you haven't ready the first part, I'd highly encourage you to do so.

Last time, we discussed four different strategies for cracking the Fallout 4 hacking mini-game. As you may recall, our four strategies are as follows:

  1. Guess randomly.
  2. Guess the word which is closest to the others, according to the Hamming distance.
  3. Guess the word that is farthest from the others.
  4. Guess the word which will result in the highest expected number of word eliminations from the list.

We also looked at an example for which these different strategies yielded different guesses. So, if these strategies really are so different, which one should we choose?

Let's answer this question experimentally. There are a couple of different metrics we could use to determine the "best" strategy. One way would be to calculate what percentage of the time each strategy is able to identify the password in four guesses or fewer (remember, in Fallout 4, you only have four...

Fallout 4 Math

If ever you've wished to experience a 1950's aesthetic combined with a post-apocalyptic landscape filled with death and decay, then the Fallout series may be right up your alley. What began with the well-received release of Fallout in 1997 has since evolved into one of the most popular video game franchises around. The latest entry, Fallout 4 was released last year to critical and commercial acclaim. Here's just one sample of the praise lavished on this game (NSFW, unless you're allowed to watch monsters get shot in the face at work):

Fallout 4, like many of its predecessors, features many sidequests and mini-games meant to hold the player's attention long after the main campaign has been completed (or, depending on play style, to postpone completion of the main campaign for as long as possible). The one I'd like to talk about today is the hacking mini-game, in which players attempt to "hack" computers in order to find loot or unlock secrets near their location.

The hacking mini...

Why is π Irrational?

I've written about my (not super positive) feelings towards π day in the past. I don't want to rehash those arguments; if you're curious, you can read some of my thoughts here, here, and here.

At the same time, I feel less curmudgeonly these days, and if your idea of a good time is memorizing a sequence of numbers and reciting them or putting them to music, more power to you.

But if we're going to let π steal the limelight from other deserving irrational numbers, let's at least explore something more interesting than its decimal expansion. Here, I'd like to provide a little visual aid for exploring a proof of the irrationality of π.

π's irrationality undoubtedly contributes to some of its popularity: after all, every rational number's decimal expansion eventually terminates or repeats. This is why nobody is impressed if you can recite the decimal expansion for 1/3 = 0.33333333… from memory. The decimal expansion of π, on the other hand, lacks this sort of simple pattern.

Just because...

For Blockbuster Movies, Is Winter the New Summer?

When I was in high school, I very much wanted Star Wars Episode I to crush Titanic and become the highest-grossing domestic film of all time. Even though Episode I was, by most acccounts, terrible, I still paid to see it several times in theaters. Alas, my efforts were in vain; the film didn't even come close to toppling Titanic.

What a difference a good Star Wars movie makes. It only took 15 days for The Force Awakens to cruise past Titanic's domestic total, and just 20 days for it to surpass Avatar as the highest grossing domestic film of all time. (Though these numbers are not inflation-adjusted; if we adjust for inflation, The Force Awakens has passed Avatar, but not Titanic).

If you consider what are now the top three highest grossing domestic films of all time, you may notice a pattern. Despite summer being well-known as the season to release potentially record-breaking blockbusters, The Force Awakens, Avatar and Titanic were all released during the holiday season. This led me...

Do Extra Innings Games Predict World Series Longevity?

Now that baseball season has ended, I find myself going through withdrawal. And with spring training several months away, I need something to fill the void left in my heart. To that end, let's take a moment and look back – with a mathematical eye, of course – on the 2015 World Series.

In case you missed it, Game 1 was one for the record books. The New York Mets and the Kansas City Royals duked it out for 14 innings. This was long enough to take the crown for the longest Game 1 in World Series history (though it tied Game 2 in 1916 and Game 3 in 2005, which were also 14 innings long). Here are the highlights:

Even before Game 1, many pundits predicted that the series would last a full seven games. For example, all 5 members of the CBS Sports staff polled in this article predicted a seven-game series, though they were split on which team would emerge victorious.

It shouldn't be surprising, then, that after Game 1 analysts maintained their faith that the series would be a long one...

Cards with Mathematics

I'm a sucker for a good card game. Or even a bad card game, if it's played in the company of good friends. Or even a bad card game played in the company of poor friends, as long as the food is decent.

Because of this relatively low bar, I've played a variety of card games. And some of these games have sparked interesting mathematical questions. If you've taken a probability course, for instance, you may have explored the intersection of cards and mathematics a bit. Maybe you had to calculate the probability of being dealt a full house in poker, or of busting in a game of blackjack.

But mathematics exists even in card games that don't typically come up in math class. And just because a deck of cards doesn't have any numbers on it, that doesn't mean it should be exiled into the realm of the non-mathematical.

To prove this point, consider Cards Against Humanity (or, if you'd prefer, its more family-friendly predecessor: Apples to Apples). In order to understand the rules of the game...

Why You Should Have a Kid in 2016

I would start off by apologizing for the clickbait-y title, but I'd rather not take any of the blame. Instead, I'll use Numberphile as a scapegoat, since one of their most recent videos inspired both the title and the content of this post.

The video in question is titled Why 1980 was a great year to be born… but 2184 will be even better. Like many who are mathematically minded, I couldn't help but watch. In the video, Matt Parker talks about a mathematical property of the year 1980. If you've got a few minutes, here's the full video:

And here's the Cliffs Notes version. Basically, Parker says that being born in 1980 is awesome, because he'll turn 45 in the year 2025, which is 452. This birth-year property hasn't occurred since 1892 (people born in that year turned 44 in 1936 = 442), and it won't happen again until 2070 (people born in that year will turn 46 in 2116 = 462). To be sure, it's a pretty nerdy reason to get psyched about being born in 1980, but I can't begrudge the man...

Hello, World!

Hi there! How are you? It's been a while. You're looking good, is that a new shirt?

Well, enough about you. Let's talk about Math Goes Pop. As you may have noticed, the output lately has been - to put it kindly - a little slow. Part of the reason for this is that I've been spending some of my free time retooling the blog. As a Tau Day gift, the fruits of my labors are now laid bare here before you.

Math Goes Pop has been rebuilt from the ground up. Aesthetics aside, the site is much the same as it was before, but hopefully feels a little cleaner and works a little better. I'd also like to tip my hat to Mira Gomha, who designed the new logo. If you want to see more of her work, you can check out her portfolio or give her a shout on Twitter.

Now that Math Goes Pop has a shiny new coat of digital paint, you can expect to see musings from me on a somewhat more regular basis. For now, I'll just leave you with a small puzzler that came to mind as I was migrating all the old posts from...

Give it Away, Give it Away, Give it Away Later

For hockey fans, summer is a quiet time of year.  I've never followed the sport that closely, but with the Kings having recently won the Stanley Cup for the second time in three years, I'm reminded of a curious incident that I witnessed during the only NHL game I've ever been to.

A friend of mine received free tickets to a Kings game when I was living in LA several years ago. He invited my now-wife and me along, and the price was certainly right, so four of us went to the Staples center one Saturday afternoon.

I don't remember much about the game (though I do recall that the Kings emerged victorious). What I remember most vividly was that during one of the breaks between periods, a new car was brought onto the ice and there was a contest to give that car away.  Sort of like what happens in this video, but the rules were a little different:

In the game I attended, six contestants were given a key to a new car, but they were told that only one key would start the vehicle. One at a...

Keeping it Real: An Addendum

Last week, Dan Meyer invited the folks at Mathalicious to opine on the meaning of the phrase "real-world," not as it applies to MTV shows (though that would make for a great conversation), but as it applies to questions asked of students in a math classroom. This week, we responded, continuing what I believe to be an important and interesting discussion about the nature of what we mean when we demand that mathematics be made more "real" for our students.

Most of my thoughts on the subject are encapsulated in the Mathalicious response. (Both articles come highly recommended, and what I say below may not make much sense if you haven't read them first.) The conversation got me thinking, though, and so I'd like to offer my own personal aside/addendum.

When I began writing in this corner of the internet in the summer of 2008, my goal was simply to talk about mathematical ideas in a way that was accessible for a general audience (and in particular, an audience that didn't necessarily think...

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