As Smart as Einstein

I’m smart. I mean, really smart. I may not be as smart as Jeffrey Skilling, who described himself as “f**king smart,” but I think I’m at least as smart as Albert Einstein.

Watch. I’ll prove it.

Einstein came up with the formula E = mc². Luckily, I’ve studied algebra, geometry and graph theory, so I know that E = edges, m = slope, and c = length of hypotenuse. I can then use the following diagram to verify Einstein’s formula:

It’s quite easy to see that the slope of the hypotenuse is 1, so plugging values into the formula gives the following:

This result is then confirmed by counting the edges in the triangle. Q.E.D.

(By the way, qed is derived from a French word that means, “And there you have it.” It’s a great Scrabble^® word, since it contains a q but no u. You should use it next time you play Words With Friends. Seriously, your opponent will be impressed.)

See? I told you I was smart.

My Scrabble™ Dilemma

My friend Andy and I used to play Scrabble™ several times a week. But he now lives in Vancouver, so I downloaded the Scrabble Free app for my Android phone, and now we play electronically.

But then I noticed that the app has a “Play Random Opponent” option. I press the button, and a game between me and WordMan26 is immediately in progress. Except for completely killing my productivity at work, this is an awesome feature. At any given time, I may be involved in as many as eight games.

Well, yes, in fact, I am addicted. What’s it to ya?

Yesterday, I was playing a game against CatLady356, and I was getting my ass handed to me — she scored a bingo on her first turn with VEHICLE and collected 188 points. Ouch! I thought I was back in it when I countered with HOARSELY for a bingo and 70 points on my first turn, but then she got another bingo with GEEZERS for 85 more points. After a few more turns, I found myself trailing 323‑218.

This is what the board looked like:

That’s when I was presented with a dilemma. On my rack, I had the letters U, N and T, which fit vertically between HOARSELY and GEEZERS to form HUG, ONE and MEDIATE. So if I were able to create a word of the form *UNT and cover the Triple Word square, I’d score at least 36 points.

Guess which other letter I had on my rack?

In my mind, CatLady356 was an elderly woman who would be offended by the word I was considering. I imagined taking my turn and then having the game sit idle while I waited for her to take her next turn. Three days would pass, then four. A week would go by. Then another. And the entire time, I’d be thinking, “Did CatLady356 have a heart attack when she saw *UNT on the board?”

Was that kind of stress worth 42 points?

I decided it wasn’t. Instead, I played TIC across the I in VEHICLES, which also made TAE and COY, scoring just 19 points.

Within minutes, CatLady356 played her next turn. She placed SODOMIzE using the S in ACOLYTES, earned 66 points, and was now leading 389‑237. And in the chat box, she left me a message:

Suck it! Vulgar words rock!

So much for overthinking my turn.

Perhaps I should instead adopt the philosophy of Fran Liebowitz:

Children are the most desirable opponents at Scrabble, as they are both easy to beat and fun to cheat.

In the course of writing this post, I reconstructed the game using Scrabulizer. If you’re a word freak, you have to check it out.

In our game, CatLady356 played three bingos, and I played two. That seemed pretty good. So it got me to wondering:

• What’s the highest score that’s ever been attained in a Scrabble game?
• What’s the highest possible score that could be attained?

On October 12, 2006, Michael Cresta scored 830 points in one game. His opponent, Wayne Yorra, scored 490 points. These tallies set records for the highest individual score (830 points), the highest combined score (1,320 points), and the most points for a single turn (365 points for QUIXOTRY, which covered two Triple Word squares).

As for the highest possible score, it seems that may still be an unsolved question. On the Scrabulizer blog, Arian Smit has a nice discussion of what he believes is the highest-possible single play: SESQUIOXIDIZING for 2044 points.

I reckon I’ll never score anywhere close to that… especially if my conscience continues to prevent me from playing slightly offensive high‑scoring words.

Sentences Are Commutative, Words Are Not

While playing Scrabble^® on my phone today, I had a rack with following letters:

AABEILN

Near the top of the board was TAVERNA, and it was possible to hook above the first six letters or below the first two letters. There were other spaces on the board to place words, but this was clearly the most fertile. The full board looked like this:

On my rack, the letters weren’t in alphabetical order (as above), so I missed a seven-letter word that would have garnered 78 points. Instead, I played ABLE for a paltry 13 points.

After my turn, the Teacher feature showed me the word I should have played:

ABELIAN

Kickin’ myself. I’ll get over not seeing BANAL, LANAI, or even LEV. But how does a math guy miss ABELIAN? I would not put up a fight if someone wanted to rescind my Math Dorkdom membership card.

What loves letters and commutes?
An abelian Scrabble player.

(That’s a joke. Please don’t play Scrabble while driving.)

A Math Geek Gives Thanks

My life is pretty good. I mean, sure, I wish I were better at Scrabble^®, or a little smarter, or a little faster, or a lot better looking. But don’t we all? Overall, I really can’t complain.

For instance, I get to write a blog about math jokes, I get to do math every day for a living, and I know that the proper amount of time t, in minutes, to cook a turkey is given by the formula t = 38 × w^2/3, where w is the weight of the turkey in pounds. And all of that is pretty cool.

I’ve not been as happy lately as I probably should be. Thanksgiving seems like the right day to reverse that pattern and recount all the things in life for which a math geek like I should be grateful. Feel free to let me know what you’re grateful for, too.

• For twin sons who love math almost as much as their daddy
• For my sons getting so excited that they speak faster than I can possibly understand (especially when they’re excited about math)
• For a wife who’s willing to tolerate a schlub like me, and who makes it very easy to keep loving her
• For grocery store tiles of the perfect size, so that your natural stride length perfectly aligns with light and dark squares
• For the wonderful safety of numbers
• For getting lost in a challenging problem
• For going to bed with a challenging problem, and waking up with the solution
• For MathWorld
• For cheesy math jokes
• For people who appreciate cheesy math jokes
• For good health
• For Nurikabe
• For friends who know what a scoober, a thumber and a blade are
• For Excel^®
• For all of the amazing people at Penn State who are not currently garnering headlines but are doing wonderful things for society
• For eyesight, to see the mathematical beauty in the world
• For teachers, and for anyone else who is willing to share their knowledge
• For disappointment, which reminds me to appreciate all the good things that I already have in my life
• For cell phones and free long distance
• For serendipitously changing the channel to a football game with five minutes left when Tim Tebow has the ball
• For zizzes, and for the word zizz
• For Scrabble^® (and more recently Words with Friends)
• For finding a parking spot with time still left on the meter
• For placing the last piece of a puzzle
• For having a really great original idea
• For friends who save me six seconds by pulling a beer out of the cooler and tossing it to me rather than walking over and handing it to me; and, for friends who trust that I’ll catch it
• For clever food names, like the “Muddy Pig” (mini-donut with Nutella and bacon crumbles) at Union Jack Pub in Harrisonburg, VA, or “Devils on Horseback” (chutney-stuffed dates wrapped in bacon)
• For ordering a beer you’ve never heard of, and finding that it’s your new DOC (drink of choice)
• For usually making good decisions
• For having things happen that aren’t all that bad when I’ve made poor decisions

Unique Words

Using Scrabble^® tiles, my sons were making anagrams. One would select four tiles, and the other would have to rearrange them to form a word.

This struck me as interesting, so I posed the following question to them:

Take four consecutive letters from the alphabet, and rearrange them to form a common English word.

How many solutions do you think there are? Before you solve the problem, take a guess. Can five words be formed from four consecutive letters? Maybe ten words? Or fifteen?

Okay, now solve the problem. Take your time. We’ll wait for you.

There are 23 ways to select four consecutive letters, and each set of four letters can be arranged in 4! = 24 ways. With 23 × 24 = 552 possibilities, it seems like there ought to be several solutions.

Were you as surprised as I was to find that there was only one?

But maybe I shouldn’t be too surprised. Lots of things in life are unique…

Always remember that you’re unique, just like everybody else.

Student: Do you believe in God?
Professor: Yes — up to isomorphism!

Then again, lots of things aren’t unique…

Don’t think you’re special. Even if you’re 1 in a million, there are still 7,000 people in the world just like you.

Here are two unique, non-math jokes…

How do you catch a unique rabbit?
Unique up on it.

How do you catch a tame rabbit?
The tame way!

Square Deal

Recently, my twin sons Alex and Eli have taken a shine to crossword puzzles. They’re only 3½, but they love letters and words, so I started making up crosswords for them using a free online crossword puzzle maker. I construct clues based on things they know — for instance, REMY is the answer to the clue OUR DOG, and IDAHO is the answer to the clue STATE NAME WE CAN SPELL WITH OUR BATH TUB LETTERS. (They have a set of foam alphabet letters, but each letter A‑Z occurs only once, so it’s not possible to spell any words with repeated letters.) They don’t quite have the motor skills to write the letters, so they read the clues and spell the answers aloud as I fill in the grid.

Tonight, I asked if they’d like to help me make a crossword puzzle. I drew a 3 × 3 grid, and I asked, “To make a crossword puzzle, you have to fill in words both down and across. Can you give me a word with three letters?” Eli suggested TOW, which I used in the first row of the grid:

T	O	W

 

Then I asked, “Okay, so the word in the first column starts with a T. Can you think of a three‑letter word that starts with a T?” Never one to overlook the obvious, Eli suggested TOW again. I filled it in, and we moved to the middle column. “Can you think of a three‑letter word that starts with an O?” Alex suggested ONE. Eli immediately realized that we could now add an E at the end of the middle row to make ONE. At that point, eight of the nine squares were filled. I pointed to the third column. “Can you think of a three-letter word that starts with a W and an E?” Eli shouted WET, and the grid was complete:

T	O	W
O	N	E
W	E	T

 

Eli then pointed out that ELI contains three letters. “Let’s make another one!” he said. So we did:

W	E	T
E	L	I
T	I	E

 

Alex then requested that we make a 4 × 4 grid that included his name, and I was very impressed with the grid that they concocted:

I	O	W	A
O	V	A	L
W	A	V	E
A	L	E	X

 

I told you that story mainly because I like talking about my sons, but also because it leads me to a cool puzzle that I think you’ll enjoy.

Use the point values for each letter as in the word game SCRABBLE:

• 1 point: A, E, I, O, L, N, R, S, T, U
• 2 points: D, G
• 3 points: B, C, M, P
• 4 points: F, H, V, W, Y
• 5 points: K
• 8 points: J, X
• 10 points: Q, Z

Create a 4 × 4 grid composed of common English words (you can use the list of official Scrabble four‑letter words** as a reference) such that the sum of the point values of the 16 letters is as high as possible.

The 4 × 4 grid that my sons created would be disqualified, because IOWA and ALEX are proper nouns. That aside, it contains four A’s; two O’s, W’s, V’s, L’s and E’s; one I; and, one X. If it were acceptable, it would be worth 35 points.

I was able to create a grid with a sum of 62 points. I’m sure that better grids are possible. What’s the best that you can do?

** Special thanks to Veky Edgar, who pointed out that the list of four-letter words appearing on my web site was incorrect. The list has been updated, and I’ve stolen it from a more credible source this time, so I believe it is now correct.