Difference between revisions of "2023 SSMO Relay Round 4 Problems"
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==Problem 2== | ==Problem 2== | ||
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==Problem 3== | ==Problem 3== | ||
Latest revision as of 15:25, 2 May 2025
Problem 1
Martha starts out with the number 
on her calculator, which has three buttons that multiply the current number by 
, 
, and 
respectively. She randomly presses one of the buttons four times. After these 
presses, she cubes the number. The expected value of the final number is 
for relatively prime positive integers 
and 
Find 
Problem 2
Let 
TNYWR. Let 
Suppose that 
points are chosen on the sides of a triangle with area 1 such that there is at least one point on each side. Let be the area of the polygon formed by connecting the points in counterclockwise order. Find the expected value of 
(Note that 
)
Problem 3
Let TNYWR. 
numbers are chosen from the set 
with replacement. If the probability that the median of these numbers is greater than 
is 
such that the decimal representation of 
has 
's before the first nonzero digit of it, find 
rounded to nearest multiple of 
