Forgot password? New user? Sign up
Existing user? Log in
Ram has 2018 coins.
The 1st coin has a 21 chance of flipping heads, the 2nd coin has a 31 chance of flipping heads, the 3rd coin has a 51 chance of flipping heads, continuing such that the kth coin has a p(k)1 chance of flipping heads, where p(k) is the kth prime number.
Ram flips each of his coins once.
What is the probability that Ram flips an even number of heads?
Are you sure you want to view the solution?
From a string of length 1 m, we choose a length uniformly at random between 0 m and 1 m, and cut as many of these lengths as possible from the string.
What is the expected length of the remaining string (in meters)?
Bonus: If we have a random number a chosen with uniform distribution over the interval (0,n1], where n∈N, what's the expected value of the remainder 1moda for a particular n?
Are you sure you want to view the solution?
For m>1, it can be proven that the integer sequence fm(n)=gcd(n+m,mn+1) has a fundamental period Tm. In other words, ∀n∈N, fm(n+Tm)=fm(n). Find an expression for Tm in terms of m, and then give your answer as T12.
Are you sure you want to view the solution?
f(n) is the number of intersections of diagonals inside a regular n-sided polygon.
For example, in the diagram, f(6)=13.
Which is larger, f(2017) or f(2018)?
Are you sure you want to view the solution?
The Brilliant logo is similar in appearance to a Disdyakis triacontahedron, a Catalan solid. Suppose we had a circuit consisting of the edges and vertices of one of these solids, and the resistance along any edge is 1Ω.
The North and South pole vertices of this solid each have 10 connected edges. Determine the equivalent resistance between the poles of the solid in Ω.
Are you sure you want to view the solution?
Problem Loading...
Note Loading...
Set Loading...