Mock AIME 1 Pre 2005 Problems/Problem 6
Problem
A paperboy delivers newspapers to 10 houses along Main Street. Wishing to save effort, he doesn't always deliver to every house, but to avoid being fired he never misses three consecutive houses. Compute the number of ways the paperboy could deliver papers in this manner.
Solution
We can find a recursion. Let be the number of legal delivery sequences for
houses. If a sequence ends with a delivery, we simply append one to
. If it ends in
nondelivery, we append a nondelivery and a delivery to
. If it ends in
nondeliveries, we append them and a delivery to
. So
.
Thus, since clearly ,
,
, we have
,
,
,
,
,
,
.
See also
Mock AIME 1 Pre 2005 (Problems, Source) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |