Wednesday, January 26, 2011


One of Monique and John’s Christmas gifts to us was Bananagrams, a Scrabble-like word game—and in selecting this item they once more proved that often it’s the small gifts (this one around $15) that bring the most lasting pleasures to the recipients. Ever since the 1960s, our whole family has been much devoted to My Word, a word-guessing game played on paper. Over the decades we’ve expanded, indeed much improved the game. We have versions where one can guess eleven-letter words. Brigitte and I also go through crossword puzzle phases—printing out three at a time from various sources and then solving them, usually in the summer, out back in the shade of the umbrellas. We’ve also made crossword puzzles—of which the most famed was one New York Times-style Sunday crossword puzzle prepared for the occasion of my Mother’s eightieth birthday. Bananagrams fits right into this matrix. The game offers a puzzle, a creative challenge—and you can easily play a round over lunch, for instances, without taking too much time.

The game consists of 144 tiles with letters. Fifty-four are vowels, E having the greatest frequency (18). J, K, Q, X, and Z are minorities; they appear only twice. The mission of the game is to use all letters the player receives in a crossword or Scrabble-like formation.

We’ve devised our own version with our own rules for measuring excellence. We divide the tiles in half and then we use our 72 tiles to make a puzzle. The result is judged by the density of the structure—the smallest possible square or rectangle—and by the average length of the words: the higher the average, the better the score. Here is the winner from yesterday’s game, laid by Brigitte.

This layout turns out to fit into an 11 x 11 square, thus 72 tiles occupying an area of 121. Seventy-two, of course, is the virtually unreachable perfection—no blanks at all. Next we calculate the average word-length, done by counting the total words (22), the tiles they use (107), and dividing tiles by words. Here the result is 4.864 (best to use three decimals). Believe me, that’s a pretty high score. This puzzle has one 10, two 9s, one 8, one 7, and three 6-letter words. That’s as far as we’ve come in developing a scoring system.

We permit any formation spelled correctly, including abbreviations that might appear in crossword puzzles. You might take exception to YA in the lower right, but a crossword creator would clue that as: “Fully grown person but not yet middle-aged (abr.)” And yes, I noticed. Troglodyte is misspelled. But that could be fixed. Challenge to the reader: How would you do it? By the way, it can be done while still staying within the 11x11 square, the word-count would remain the same, and the unsightly doubling of AXIS would also be fixed.

Abraham Nathanson created Bananagrams and introduced it in 2006—thus virtually yesterday. Nathanson passed away at age 80 in 2008. He was a graphics designer. Thanks, Abraham. Nice contribution to the peace of the world.


  1. For shame! I pride myself at being a pretty good speller...but find that I am a troglodyte instead...

    But I have corrected the puzzle since and Arsen has generously accepted the change.

  2. I have to admit that not only do such things fascinate me, but I go further and treat the result as some sort of Bible Code thingie....

    Thus, I see "denigrate" and "machine" for a reference - very arcane - to "luddite" and "sabotage".

    The fact that you have "axis" and "axis" points to a geometry of only 2 dimensions along the x-axis and the y-axis; the z-axis is missing and is, hence, a "hidden dimension".

  3. Montag: Your hermeneutic powers are astounding!

  4. I'm so glad that you two are enjoying this as much as we'd thought you would, or more!

    Now, down to business...

    Remove the letter X, I, and S from the first (top) instance of AXIS.
    Romove the Y from the word SAY at the bottom and place that letter into its rightfull spot in TROGLODYTE.
    Place the X where the Y had been in SAY.
    Place the S at the end of DENOGRATE.
    And finally, place the I inbetween the B and the A in the workds DIRIGIBLE and REAM to creat BIA as in Bureau of Indian Affairs.

    What fun and I learned a new word too, Troglodyte!

  5. Very good, Monique! Disposition of that X in AXIS is the real problem, and, yes, SAX is the solution to that. They left-over IS is less of a problem, and your solution is very neat. I like BIA. Mine, once past SAX, was slightly different...


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