Simon’s Cat

As a gamer, the holidays give me opportunities to play games with non-gamers. People like my family. Or, more relevantly to this article, people like my niece. Here’s what you need to know about my niece: she is 6 years old who really loves to play games, begot from gamer parents. This year we played Simon’s Cat. hedgehogsAnd because she is 6, we played Simon’s Cat a lot. (The hedgehogs were my favorite.) And, as a mathematician and a gamer, I have to say that Simon’s Cat has a fair amount of game for its simple rules system.

Playing games with a 6 year old, as an adult, can be challenging. Mostly because they aren’t playing games at this age. They are playing experiences. Chutes and Ladders is most definitely an experience, not a game. Despite all those fabulous ladders and exciting chutes, the game is just a very complicated randomizer. It’s basically the Rube Goldberg machine of coin flips. It hurts my brain when a child is sad because they “lost” experiences like this. I just want to say, “You only had 1/2 a chance. There was literally nothing you could do to avoid this fate.”

I think a game gets to be called a game if and only if the choices you make as a player influence your ability to win or lose.   So, the question of the hour is: Is Simon’s Cat a game or an experience? Let’s cover the components and the rules.  Here are all the cards in the deck arranged in a pleasing way:


You are dealt a portion of the deck. Whomever has the Pink Cat 3 plays it to the center.  Next, you go around the table and if you have a card that is the same color or the same number, then you can play it. If more than one card is playable, then you pick which one to play.  If you don’t have any cards that you can play, you collect all the cards from the middle of the table. These cards all count as 1 mess that you had to clean up. If you collected a mess, then you play any card you want to the table.  Suffice to say, you play a card every time it’s your turn, but you want to collect as few messes as possible. Once all the cards are played, the player with the fewest messes wins! Got it? If you want the official rules, you can find those here.

A game has a game if and only if the choices you make as a player influence your ability to win or lose.

In order for this to be a real game, my choices have to influence my chances of winning.  Thus, there must to be some strategy to the order I play my cards that is better than another.  Is my chance of winning higher when I use a good strategy than it is for me to randomly chose a usable card?

A slightly different way to ask this question is: Are some cards more valuable than others? Can some cards be used in more situations? If there are cards which are more valuable, then I want to keep those in my hand as long as possible for increased flexibility in the late game.  However, if all cards are equally valuable, then there won’t be a ‘better’ or ‘worse’ strategy and Simon’s Cat isn’t a real game (as far as I’m concerned anyways!)

gnomesSince I can only play a card if the previous card shares a color or number, I want to know which card has the most other cards which share a number or color: the most similar cards.  Let’s consider the Gnomes. There are only two Gnomes in the game. At first, this may appear to be valuable. (Because you can block others perhaps?) But remember, your main goal is to not get messes. So, you are most concerned with whether a card is playable by you or not. The Green Gnome 1 is only playable off of the Green Gnome 2, Orange Mouse 1, and Purple Dog 1. This means there are three cards in the deck which can precede the Green Gnome 1.

What about my personal favorite, the Yellow Hedgehog 3? Yellow Hedgehog 3 can play off of any of the five other yellow cards or any of the four other 3s. Thus, there are nine cards that a Yellow Hedgehog 3 can play off of. This means that between Green Gnome 1, with three similar cards and Yellow Hedgehog 3, with nine similar cards, the Yellow Hedgehog 3 is a more valuable card. Except, these can’t be used in the same situation.  So, we’ve shown that cards have different valuable-ness, but we haven’t shown that this will ever matter.

Let’s consider an example.  Let’s say the card played before my turn was a Yellow Hedgehog 3.  I have a Blue Kitten 3 in my hand and an Orange Mouse 3.  Which one should I play? Well, the Blue Kitten 3 has eleven similar cards.  Orange Mouse 3 only has seven.  Assuming we don’t know any more information about what was played previously, it would be a better choice to play the Orange Mouse 3 because there are more cards that can trigger my Blue Kitten 3 than my Orange Mouse 3. So, in this moment of our investigation, we know that there will be a strategy which is better than random. That means Simon’s Cat is an actual game! I can make a better or worse decision. I can impact my fate! Thank you, Steve Jackson Games, for making a simple game (without reading!) that is still a game. Seriously. Thank you.

Before we go into the bonus lightning round, I have to insert an aside for the other gamer mathematicians out there: for surely you have already determined that which card is the most valuable is not just a function of the total cards in the deck, as I presented above.  Returning to my example: if all the other Blue cards had already been played, then (in that moment) the Orange Mouse 3 is actually a better play because, at the moment, Blue Kitten 3 is not at the top of her game.  All her friends have already been played to the table!  So, she is less valuable.  To those of you who thought of this, excellent work! Your insight also further proves that there is a real game to be had here.

Now for the first bonus round:

Bonus Question: Which card begins the game as the most valuable card? Can you figure it out by looking at all the available cards in the deck?  You can go look. Take a guess!

Answer: Hopefully you figured out it had to be a Pink Catsimon_cat3 because Pink has the most cards in its color.  And the most valuable card should also be a 3 or 4 so it shares the most colors across a single number. Thus, the 2 most valuable cards are the Pink Cat 3 and Pink Cat 4.  Except you will never get to play the Pink Cat 3 on another card, because it must be played first.  Thus, the most powerful card is the Pink Cat 4. Notably, Pink Cat 4 is the only Pink Cat who isn’t doing something crazy in the graphic on the card.  Therefore, I am left with no other option than to assume that Simon’s real cat is Pink Cat 4.


And the final bonus round:

Reader be warned! It is very possible to be dealt a hand of cards and preceding cards in a way which allows no choices. In this situation, we, the adults, suck it up and “play” our gaming experience. Simon’s Cat has more game than most of the games I played over the holidays, but it’s still a game which can be explained in 3 sentences. It’s bound to have some flaws. For a game which can be played with pre-readers, it gets high marks from me!

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Alternate Mathematics

Alternate Mathematics: sometimes things seem too good to be true. #AltMath


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Those Topologists…


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Older and wiser


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Ugly Fact


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Penny Pinching at the Grocery Store

When I’m at the grocery store, I almost always compare the prices of different sized packages.  How much less per oz does it cost when I buy twice as much?  Sometimes the price is notably different.  Usually the cost gets cheaper when I buy more.  Here are some quick numbers I pulled from Target about Cheetos.

Cheetos Data
OZ Price $/oz
2.375 1 0.42
3.7 1.49 0.40
8.5 3.39 0.40
17.5 3.99 0.23

Sure enough, as I commit to more Cheetos, the price per oz decreases. This is almost always true! Except when it isn’t. Imagine two sizes of flour: an 8oz and a 16oz.  When the smaller bag costs $2.99 and the larger costs $5.99:


In this situation, you are saving exactly 1 penny if you buy two small bags instead of one large bag. Maybe this isn’t enough to make you change your habits, but I always buy 2 packages of the smaller product when I see this. Always. I’m sure some of you have done this too! Because a penny saved is a penny I have righteously stolen from the grocery store which so vilely priced their products ridiculously!

Actually, I can’t decide if I feel exceptionally clever when I do this… or like I’ve just wasted 5 second of my life over optimizing something trivial.  The opportunity cost of those 5 seconds is surely worth more than a penny? Right?

Well, let’s find out.  If I managed to earn 1 cent every 5 seconds, I would be earning $7.20/hour.  Not bad! But not great.  So maybe it’s not the worst thing to do while I shop.

Now, my dear reader, I have to share with you that this post came out of personal experience.  Yesterday my dad just bought 2 bags of chocolate chips, instead of one, to save a penny. And then he wrote an email to the rest of the family to tell us about it. Does your dad do that too? In his mind: The time spent on the consideration of this penny does not increase the time spent shopping …and he’s going to think about something anyway. So perhaps he is right. It’s a penny saved with zero opportunity cost! And that’s a magical thing by itself. And how often can you say your grocery trip was magical?

But, in all reality, despite the original effort resulting monetary benefit… the accounting of the event is probably not worth much. So now that I have spent time writing emails to my father and even more additional time writing a blog post to you? What have we gained from that effort? Well, maybe we all feel just a little bit better every time we gleefully pick up two tiny packages that magically cost less than the larger version of the same thing.

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Hidden Figures

Hidden Figures, the movie, enjoys its wide release today. I got to see the film last night. Janelle Monae, Taraji P. Henson, Octavia Spencer out shine the stars in this beautiful film.  Hidden Figures is based on the book which was released in mid-2016.


The movie was so anticipated, it was actually optioned before the book was even published. 2016 produced two amazing books about female computers and their contributions to the space race: Rocket Girls and Hidden Figures. Rise of the Rocket Girls focuses on the female computers in southern CA at Jet Propulsion Laboratory (JPL). Hidden Figures follows the black women in Langley, Virginia who were computers for NACA and later NASA. Both books are excellent! And I highly recommend both of them. Go get them. Right now. It’s cool, I can wait. Got them ordered? Okay, let’s continue.

Back in the 1930’s women who liked math had limited career options: teacher, nurse, or secretary. These are the same options for all women, excelling math did nothing for you. Except, a woman could, in very particular circumstances, be hired as a computer. Because before computers were machines, computers were people who computed things.  This complicated task often fell to women because it was considered basically clerical. That’s right: computing triple integrals all day long qualified as clerical. And, gosh, how many of us could do that today? Not many! I, for one, can’t do very much without the help of a machine computer. (I have been advocating for the benefits of using calculators for basic math for a while!) Without these highly skilled women putting pencil to paper, we would not be able to complete the most challenging orbital computations of the day.

Karl Zielinski: Let me ask you, if you were a white man would you wish to be an engineer?
Mary Jackson: I wouldn’t have to, I’d already be one.

Hidden Figures, the film

Women often couldn’t move up. Neither to management or to more challenging technical roles like engineering or mathematics. They were forever stuck in their role as a computer. Mary Jackson, one of the key characters in the narrative wishes that she could be an engineer. But “most of the country’s top engineering schools didn’t accept women. …As for black female engineers, there weren’t enough of the in the country to constitute a rounding error.” (Hidden Figures, Pg 144). The film chooses to make this a key plot line. Obviously the issues of today influence this choice, because black women are still struggling to get their fair shake at the jobs white women have worked at for decades.

On top of societal prejudice, there was also legal bounds holding these black women back. Segregation in all public life was standard at that time. And being that Virginia is in the south, segregation was even more ingrained in the laws and society. This was one of the pieces of magic that took place at Langley, in Hidden Figures. “Unlike public schools, where minuscule budgets and ramshackle facilities exposed the sham of “separate but equal,” the Langley employee badge supposedly gave Mary access to the same workplace as her white counterparts.” (Hidden Figures, pg 108) But, despite that, the women have to fight for each and every injustice to be removed. And I do mean each and every.  For example, they wage a silent battle lasting many months where the ladies remove the “colored” sign from the lunch table everyday only to have it return the next day. In the film, this particular injustice wasn’t highlighted, instead the film focused on the immense challenges of colored bathrooms for Katherine Goble (later Katherine Johnson).

In this way, Hidden Figures gives beautiful insights into what it was like to be a female mathematician 50+ years ago. Hidden Figures has the added layer of communicating was it was like to a black female mathematician. “Compared to the white girls, [Mary] came to the lab with as much education, if not more. She dressed each day as if she were on her way to a meeting with the president.” (Hidden Figures, pg 108). I believe the film highlights this imbalance beautifully with their costume design. There is a fabulous scene where a large group of male scientists are gathered and every one of them has on a long sleeves white shirt with a thin black tie. Katherine Johnson is with them and is wearing a modest green dress. Despite it’s modesty, she stands out of a crowd with her color, style, and poise.

The film is sharp, witty and surprisingly optimistic. If you only see 1 movie in 2017, see this one. While there are other recent films about mathematicians (e.g. The Man Who Knew Infinity), Hidden Figures has the heart to make it a classic. Because if you are black or female or a mathematician or a fan of space, this film will speak to you.  And if you aren’t any of these things… that’s okay! I won’t hold it against you.  Go see this movie to learn more about life at Langley during the biggest and only race to space there ever was.

Paul Stafford: There’s no protocol for women attending.
Katherine Johnson: There’s no protocol for man circling the earth either, sir.

Hidden Figures, the film


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