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Old 12-13-2005, 05:23 AM
Siegmund Siegmund is offline
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Join Date: Feb 2005
Posts: 415
Default Re: Crossword Puzzle

It depends how much work you're willing to do to improve your chances. Your answer is right if you randomly guess at every letter.

For a start, you can guess letters in proportion to their normal frequency of use (12% E, then T A O N R I S H downward), and roughly double your chance of getting each letter right. [If you wanted to maximize the number of correct letters, you'd fill in the whole puzzle with EEEEEE, but that would give up any chance of getting the whole puzzle right.]

Or you can go to a frequency table of digrams and trigrams, and fill in all the across clues with vaguely pronounceable-looking strings of letters. This would give you maybe a 7% chance at guessing the first letter of each word right, and then a 15 or 20% chance of getting each additional letter in the word right if you started with the right letter. That puts you at something like (.07)^40*(.15)^130 of getting the whole puzzle right.

You can do much better still if you check the digrams and trigrams in BOTH directions, and have chances approaching 25% of getting any given letter right.

Further improvements are possible if you include information about the general structure of crosswords (lower right corners of subsections will be "S" much more often than in a random letter grid for instance) or if you generated your digram frequencies by analyzing thousands of crosswords instead of using general-usage frequencies.

All of these improvements together ought to push your chances to somewhere in the vicinity of (.40)^170.
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