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 Distinct Delivery Deduction (Posted on 2014-09-04)
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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): a manua etc............. thank you | Comment 5 of 7 |
(In reply to re: a manual count solution by Steve Herman)

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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