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1232 is HERE (Posted on 2012-07-18) Difficulty: 3 of 5
Let us map all combinations of letters ( both valid words and gibberish) by a single criterion: 1st letter and all other appearances of that letter will be replaced by a digit 1, the first letter distinct from the 1st will be replaced by 2 , and so will be all other appearances of that letter , etc
Thus onion => 12312, queue => 12323, coffee => 123344 etc.

Clearly both "clue" and "ship" will be represented by a number 1234 while both "will" and "bass" by 1233.

Let us denote by a(k) the number of possible numbers of k digits.
Then a(1)=1; a(2)=2; a(3)=5 etc

1. Provide sample valid words for 1234512 and 123242526272.
2. List all the possible numbers for 4-letter combinations of letters (both valid and unvalid words).
3. Evaluate a(4), a(5), a(6).
4. Find a formula (either recursive or direct) for a(k).

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionsolutionsCharlie2012-07-18 14:16:21
Hints/Tips2,3, and 4, possible approachbroll2012-07-18 13:37:33
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