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CRYPTIC CHANCE

 
 
Reply Fri 1 Jan, 2010 02:02 am
Elmer was befuddled, his anagram solver, thesaurus, crossword puzzler and online cryptic crossword were like a koala up a gum tree: on the blink.

He sought solace from his old china plate, The Flying Dutchman and a request for an answer, ... any answer.

A little bird had told Elmer 4 of the letters that went on any of 6 remaining spaces and Elmer wanted to know how many ways those 4 letters could fit onto the 6 remaining squares.

Feel free to help?

Derivation of the general theorum earns a lifetime pass to eschew crosswords.
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Type: Question • Score: 0 • Views: 1,055 • Replies: 8
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View best answer, chosen by oolongteasup
lmur
 
  1  
Reply Fri 1 Jan, 2010 08:24 am
@oolongteasup,
I'm a-gonna Fuddge on that one.
oolongteasup
 
  1  
Reply Wed 13 Jan, 2010 02:35 am
@lmur,
and nudge nudge wink wink
0 Replies
 
markr
  Selected Answer
 
  2  
Reply Fri 15 Jan, 2010 02:27 am
@oolongteasup,
4 of the 6 squares can be selected in C(6,4)=15 ways.
Once the squares are chosen, they can be populated in
4! / (w! * x! * y! * z!) ways
where w, x, y, and z are the number of occurrences of the first, second, third, and fourth letter, and w+x+y+z=4
Obviously, if at least one letter is duplicated, there can't be four different letters - at least one of w, x, y, and z must be zero. But that's OK because 0!=1.

The answer you seek is the product of the two calculations. Assuming the four letters are unique, the answer is 15*24=360.

The general formula is easier to state when the letters are unique:
N = the number of squares
M = the number of (unique) letters

The number of ways is
C(N,M) * M! = N! / [(N-M)! * M!] * M! = N! / (N-M)!
oolongteasup
 
  1  
Reply Sat 16 Jan, 2010 04:22 am
@markr,
twice the blanks were used
perfect cover for
darting letters



markr
 
  1  
Reply Sat 16 Jan, 2010 08:05 pm
@oolongteasup,
Huh?
oolongteasup
 
  1  
Reply Sun 17 Jan, 2010 12:57 am
@markr,
the left hand column reads twice perfect darting and the answer is 360

sorry i forgot that your inclusion of the general theorum meant you get to eschew cryptic cruciverbalist stuff

congratulations

how about you resurrecting tryagain's page (that lad knew how to cut and paste) by posting an easy one so engineer and i, et al can battle it out?
markr
 
  1  
Reply Sun 14 Feb, 2010 03:53 am
@oolongteasup,
Ah! A Ton-80 times 2. I'm a former darter, but I didn't catch the intended puzzle.
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markr
 
  1  
Reply Sun 14 Feb, 2010 03:58 am
@oolongteasup,
It appears that Tryagain is back. I don't think I could do justice to his page - he is one-of-a-kind.
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