Forgot password? New user? Sign up
Existing user? Log in
A number of the form 10n−1=n times9999...9, where n is a positive integer, will never be divisible by 2 or 5.
Are there any other prime numbers that numbers of this form are never divisible by?
Are you sure you want to view the solution?
A circle is inscribed in a right trapezoid with base lengths 22 and 35.
What is the area of this trapezoid?
Are you sure you want to view the solution?
22222=22222<2
Is this true?
Bonus: Generalize the following. n timesxxx⋯x
Are you sure you want to view the solution?
A regular decagon is obtained by joining 10 regular pentagons side by side.
Generalizing this, we claim that there is a regular n-gon obtained by joining n regular k-gons side by side.
What is the sum of all possible values of k≥5?
Are you sure you want to view the solution?
A casino owner invents a new game where a player flips a fair coin n times in a row. If the player does not flip two heads in a row at any point in the n flips, then he wins the game; otherwise the house wins.
To make the game popular, the casino owner wants to maximize the player's chance of winning. However, the casino needs to make a profit, so the house must win more than half of the games played over the long run.
What should the casino owner set n to be?
Are you sure you want to view the solution?
Problem Loading...
Note Loading...
Set Loading...