On the effect of body orientation on anagramming speed

When we are standing up, gravity pulls blood down which is detected by "baroreceptors" in the circulatory system. The circulatory system compensates by increasing the heard rate, so that blood pressure in the upper body is maintained. When the baroreceptors register such a blood pressure drop, the locus coeruleus neurons become more active. The locus coeruleus responds to stress by increasing release of norepinephrine (a.k.a., noradrenaline). This has a number of effects, including increasing heart rate and blood flow and boosting motivation, thinking, and alertness. But researchers have found that increases in norepinephrine coincide with a slight slowing of certain kinds of thinking.

The thesis is that "insight problems", the kind where your brain kind of wanders and does background processing, and then suddenly presents a solution in an "A-ha!" moment, happen faster when you have lower norepinephrine levels. A simple "A-ha"-type problem to test, and one which is very popular in psychological research, is anagramming.

In one experiment [M.P. Walker, C. Liston, J.A. Hobson, R. Stickgold, "Cognitive flexibility across the sleep-wake cycle: REM-sleep enhancement of anagram problem solving", Cognitive Brain Research, Volume 14, p.317-324 (2002)], researchers woke people up at different stages of sleep and asked them to solve anagrams. They found that subjects who had just been in REM sleep were better at anagramming than subjects who had been in some other sleep stage. And REM sleep has a lower locus coeruleus activity level.

In another experiment, [D. M. Lipnicki and D. G. Byrne, Cognitive Brain Research, Volume 24, p.719-722 (2005)], researchers had subjects solve 5-letter anagrams (like unscrambling DEFSU to get FUSED) and perform arithmetic problems (73 - 58 + 19 - 26 = ?), while standing up and then while lying down. When standing up, average anagramming time was 29.4s +/- 6.3s. When lying down, average anagramming time was 26.3s +/- 5.4s. The difference in anagramming times (3.1 seconds) is smaller than the standard deviation of the data, but the statistical analysis suggests that the error bars are not that important, allowing us to conclude that the average person in the study anagrammed 10% faster while lying down.

A similar test found that standing is correlated with people solving simple arithmetic problems a few percent faster, but it's such a small difference that it doesn't seem statistically significant.

Summarizing: When you stand up, your body tends to become more alert and less relaxed, and you may anagram slightly slower as a consequence.

Caveats: This study was performed on randomly selected subjects with no proclivity for word games. When given 32 5-letter anagrams to solve, and 45 seconds to solve each in, the average number of solutions was 8 or 9 (whether sitting or standing). A typical Bananagrams player would do significantly better, I would be willing to bet.

I wonder if the cause and effect might flow the other way: if lower blood pressure allows one to anagram faster, can focusing on anagramming cause blood pressure to be temporarily lowered? Or will it just cause one to lie down?

Anagramming is only one of the skills used in playing word games, of course. The kind of concentration necessary to play Bananagrams fast most likely requires the mind to not be in a relaxed state. (And what I'd really like to see is a study on playing Bananagrams itself). Still, whenever the professional Bananagrams league launches, one of the first drugs they should consider regulating is beta-andrenoceptor antagonist propranolol.

---

Further reading:

D. M. Lipnicki and D. G. Byrne, "Thinking on your back: Solving anagrams faster when supine than when standing", Cognitive Brain Research, Volume 24, p.719-722 (2005).

If you have access to it through your library, you can get the paper from here.

How to remember the number of tiles to start off with in Bananagrams

The simplicity of Bananagrams is one of its strong points. But there is one rule that always seems to cause debate and searching for the instructions: The number of tiles that each player is supposed to begin with. The rules call for the following initial tile counts:

• 2-4 players - 21 tiles
  
• 5-6 players - 15 tiles
  
• more than 6 players - 11 tiles

I find it easy to remember the cutoffs for each level, probably because 4 and 6 are both even. And 21, the number of tiles when playing with 4 players, is burned into my memory. So here is my mnemonic for determining the other numbers: After the cutoff for 4 players, subtract 6 tiles. After the cutoff for 6 players, subtract 4 more tiles.

That should shave ten seconds off my next Bananagrams match. Plus now I am no longer bothered about losing my set of Bananagrams instructions.

Tactics to help you win at Bananagrams

Through playing many, many games of Bananagrams, I have learned a few lessons about how to approach the game:

• Concentrate on making words out of the hardest letters first to get them out of the way.
  
  
• Try to make one long word at the beginning and build off of it. In general, the longer your words are, the more places there will be to build new words.
  
  
• Particularly at the beginning, when you flip over all your letters, try to assess the balance between consonants and vowels. If it is off, you can try to make vowel-heavy or consonant-heavy words [See what to do when you have too many consonants and what to do when you have too many vowels.]. It's far better to do this from the outset, than to have a mostly-finished grid and realize that you need to go back and remodel the whole thing.
  
  
• Try to structure your grid in a more open way.
  
  Good:

     CHILL      
         I 
         POST

  Not-as-good:

     CHILL
         I
      STOP

  The former is far easier to build new words off of:
  

     A
     CHILL W
     U   I A  
     T   POST
     E      O

  We could even quantify the difference between the two approaches. In the first case, words can be build up or down (or both) from 5 letters (C,H,I,S,T) and just in one direction from 2 more (the L and the O). In the second case, there are 8 letters that one can build off of in only one direction. The number of words you can make with the H in any position (HUE, OCHRE, EACH) versus just making words that start or end with a given letter, is definitely bigger than a factor of 2... I'm going to conservatively estimate it to be 3 times larger. Then the flexibility scores of the two grids above would be 3*5+2=17 and 8*1=8. And the advantage of choosing an open structure only grows as the grid becomes larger. It's often the difference between smoothly adding letters to your grid and having to completely rearrange things.
  
  
• When you are in the peeling phase, keep in mind one or two words that you can steal letters from and positions where you can easily add tiles to make new words. Or words that you can easily anagram (with the newly peeled letter) to make a new word.
  Suppose you have the grid below and you peel an A.

       TRY
       I
       E
     FORKS

  From FORKS, you can take the S and combine it with the A to from SAY:

         S
         A
       TRY
       I
       E
     FORK

  Now that I'm thinking about FORK and SAY, I note that the K from FORK could be substituted for the more-easily-used A in SAY to form SKY. So if the next letter I peeled was R, I could quickly make that switch, freeing up the A to build the word FAR:

         S
         K
       TRY
       I
       E
     FOR
     A
     R

  At this stage, I might wind up extending FOR to FORT or FORD or FOUR or FORE or anagramming it to ROOF, depending on what letter become available. It would be nice to build SKY into RISKY. And FAR looks like an appealing place for making FARM, FAIR, or FARE.
  

The speed of Bananagrams is such that you will not be able to consider every possible move, but having just a few rules of thumb to keep you from getting boxed in can allow you to still play fast while increasing your chances of winning.

Another reason Scrabble dictionaries are inadequate for Bananagrams

The Scrabble board is a 15-by-15 grid, so naturally, Scrabble dictionaries have no need for words longer than 15 letters. Oddly even "Super Scrabble" which is Scrabble played on a larger board and with more tiles, still uses the 15-letter limit.

Some 16-letter words for your consideration:

ambidextrousness
anagrammatically
anthropomorphize
autobiographical
biodegradability
bureaucratically
counterclockwise
crystallographer
cryptozoological

I can totally see someone staring off with "clocks" in their grid, turning it into "clockwise", and then in a brilliant burst of insight, combining it with "count" and some stray tiles to make "counterclockwise". If I ever pulled that off, I would be so proud that I wouldn't even care if I won the game. (OK, I'd still care, but either way it would be awesome.)

What is the longest word that you have ever used in a Bananagrams match? For those who like games with rounds that escalate, the must-contain-an-N-letter-word would be an interesting and challenging variation. How high can you go?

Scrabble Me: The chimera of Scrabble games

I recently ran across the strangest official Scrabble mutation that I have ever seen: "Scrabble Me"

It looks like, in addition to Scrabble Apple, the makers of Scrabble decided to make another game that fuses elements of Bananagrams with those of conventional Scrabble. This one is kind of a Frankenstein hybrid, so don't say I didn't warn you.

The game is divided into rounds. In each round, everyone uses up their tiles by building words on independent mini-Scrabble-boards. Then players score their words, draw new tiles, and continue building up their grids.

Unlike Scrabble Apple, which seemed to be fairly close to Bananagrams, with some Scrabble elements thrown in (scoring and double word score squares), Scrabble Me seems like it is deviating from the Scrabble - Bananagrams continuum. It's more random, in the sense that when someone uses a blank tile (called "wild" in this game), they have to swap their grid with someone else's. However, it is less random in the sense that there is a pool of face-up tiles that one can opt to draw from, instead of from the bag. It somehow reminds me of the card game Uno.

In the interest of trying to categorize these games, I've made this ASCII chart:

   ^                     BANANAGRAMS
S  |
P  |
E  |
E  |
D  | SCRABBLE          SCRABBLE ME
   |
   |---------------------------------->
         DECOUPLING OF PLAYERS        

And there really ought to be a third-dimension where Scrabble Me towers above the others on the Uno-ness axis.

The reviews I've read are sort of favorable though. In spite of the Frankenstein quality, I would like to try this game.

Palindromes you are most likely to be able to make in Appletters

Since making palindromes earns players bonus points in the Applescore game (as described in this previous post on Appletters), I've compiled a list of the palindromes you are most likely to be able to make during the game (really short ones or ones that use common letters).

Off the top of my head, using only the minimal length examples:

bib, bob
dad, deed, did, dud
eke, ere, eve, ewe, eye
gag, gig
kook
mom
noon, nun
pap, pep, pip, pop, pup
radar
sees
tat, tit, tot
wow

And, of course, there is one Scrabble-legal letter combination that is two letters long and a palindrome: AA. A'a (pronounced /ah ah/) is a type of lava, which is thicker and more viscous than other types. It is characterized by flowing in a sporadic fashion and leaving a rough surface when it cools.

And if it's not already been suggested, then I propose a variation of Appletters called Palindrominoes: The word snake is formed as in regular Appleletters, but if you can form a palindrome where the base letter (the "head" of the snake, I suppose) is inside the palindrome, then you are permitted to position letters both above and below the end-tile, as shown in the example below:

  e   
  VIGOR 
  e   I
      N  
      KITE

Then you can give the snake multiple heads, like a hydra or a planarian or something. A little extra chaos to spice up your Appletters game.

The games of Lewis Carroll

In addition to his anagramming prowess and his wonderfully surreal and whimsical stories, Lewis Carroll is known for creating numerous games and puzzles.

He is credited with the invention and popularization of the doublet (a.k.a, Word Ladder) in which one transforms one word into another, one letter at a time, with all the intermediary steps being legitimate words. Two examples:

          EAST          CAT
          FAST          COT
          FEST          COG
          WEST          DOG

Admittedly, this is really more of a puzzle or a pastime than a game.

He spent much of his professional life tutoring students in mathematics and logic. He invented a game called The Game of Logic designed to teach the fundamentals of formal logic, using a unique way of representing logic propositions with a game board and colored tokens. The game is described in a book of the same name (available from Project Gutenberg (though they seem not to have gotten the figures right)). Ultimately though, it seems to be for one player and seems rather like a puzzle.

Carroll also thought about and devised rules for playing billiards (the British sort, played on a table without pockets) on a circular table.

In 1880, he wrote in his diary that "A game might be made of letters, to be moved about on a chess-board till they form words.". Martin Gardner (famous for his writings on recreational mathematics) took such notes from the writings of Carroll and fleshed them out into a board game in which, as I understand it, letters are placed on the first row of a chessboard and can be moved like queens to form a word in the fifth row. Meanwhile your opponent is trying to do the same thing while blocking you. (Rows 2, 3, 6, and 7 are open to everyone.) Like Scrabble, once a word has been formed, more letters are drawn from a bag, and the first row is replenished. You can buy the game here. I am thinking of playing an improvised version with a chessboard and a set of Bananagrams tiles.