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Distinct Delivery Deduction (Posted on 2014-09-04) Difficulty: 3 of 5
Art, the mail carrier delivers mail to the 19 houses on the east side of a street.

Art notices that:
(i) No two adjacent houses ever get mail on the same day, and:
(ii) There are never more than two houses in a row that get no mail on the same day.

How many distinct patterns of mail delivery are possible?

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re(2): a manua etc............. thank you | Comment 5 of 7 |
(In reply to re: a manual count solution by Steve Herman)

Thanks for your correction.

 However , the non-recursive method is generally superior to
recursive calculation.
Therefore , my amendment  is as follows.
Lets denote by F(n) the number of qualifying sentences, terminating by 1 (which are easily calculated my way).
Then the total T requested for n houses is:
T=F(n) + F(n-1) + F(n-2) 
For n=19:

(F19)= 151
(F18)=65+49=114
 (F17)= 49+37=86   CALCULATED MY WAY


you will clearly see the benefit , if the street is 119 houses long
(non computer comparison) or 4674689 houses long (computer runtime affected.)

Many sincere thanks for your comment

  Posted by Ady TZIDON on 2014-09-05 03:57:16
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