Difference between revisions of "2020 CIME I Problems/Problem 8"
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==Problem 8== | ==Problem 8== | ||
| − | A person has been declared the first to inhabit a certain planet on day <math>N=0</math>. For each positive integer <math>N | + | A person has been declared the first to inhabit a certain planet on day <math>N=0</math>. For each positive integer <math>N>0</math>, if there is a positive number of people on the planet, then either one of the following three occurs, each with probability <math>\frac{1}{3}</math>: |
:(i) the population stays the same; | :(i) the population stays the same; | ||
Revision as of 17:00, 31 August 2020
Problem 8
A person has been declared the first to inhabit a certain planet on day 
. For each positive integer 
, if there is a positive number of people on the planet, then either one of the following three occurs, each with probability 
:
- (i) the population stays the same;
- (ii) the population increases by
; or - (iii) the population decreases by
. (If there are no greater than people on the planet, the population drops to zero, and the process terminates.)
; or
. (If there are no greater than The probability that at some point there are exactly 
people on the planet can be written as 
, where 
and 
are positive integers such that isn't divisible by 
. Find the remainder when 
is divided by 
.
Solution
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Followed by Problem 9 | |
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