Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Problems of the Week
Contribute a problem- Week of December 17
- Week of December 10
- Week of December 3
- Week of November 26
- Week of November 19
- Week of November 12
- Week of November 5
- Week of October 29
- Week of October 22
- Week of October 15
- Week of October 8
- Week of October 1
- Week of September 24
- Week of September 17
- Week of September 10
- Week of September 3
- Week of August 27
- Week of August 20
- Week of August 13
- Week of August 6
- Week of July 30
- Week of July 23
- Week of July 16
- Week of July 9
- Week of July 2
- Week of June 25
- Week of June 18
- Week of June 11
- Week of June 4
- Week of May 28
- Week of May 21
- Week of May 14
- Week of May 7
- Week of April 30
- Week of April 23
- Week of April 16
- Week of April 9
- Week of April 2
- Week of March 26
- Week of March 19
- Week of March 12
- Week of March 5
- Week of February 26
- Week of February 19
- Week of February 12
- Week of February 5
- Week of January 29
- Week of January 22
- Week of January 15
- Week of January 8
- Week of January 1
- Week of December 25
- Week of December 18
- Week of December 11
- Week of December 4
- Week of November 27
- Week of November 20
- Week of November 13
- Week of November 6
- Week of October 30
- Week of October 23
- Week of October 16
- Week of October 9
- Week of October 2
- Week of September 25
- Week of September 18
- Week of September 11
- Week of September 4
- Week of August 28
- Week of August 21
- Week of August 14
- Week of August 7
- Week of July 31
- Week of July 24
- Week of July 17
- Week of July 10
- Week of July 3
- Week of June 26
- Week of June 19
- Week of June 12
- Week of June 5
- Week of May 29
- Week of May 22
- Week of May 15
- Week of May 8
- Week of May 1
- Week of April 24
- Week of April 17
- Week of April 10
- Week of April 3
- Week of March 27
- Week of March 20
- Week of March 13
- Week of March 6
- Week of February 27
- Week of February 20
- Week of February 13
- Week of February 6
What is the maximum number of chess knights that you can place on a chessboard such that none of them are attacking each other?
Note: The knights in question have no allegiance to white or black. The picture above shows knights which cannot attack each other in one move.
by
Munem Shahriar
Are you sure you want to view the solution?
3 frogs are sitting on 3 of four lily pads in a line, leaving one unoccupied, as shown below:
A frog can only move to the empty lily pad either
- by jumping to it if the frog is immediately next to the empty lily pad, or
- by leaping over one frog if the frog is two seats away from the empty lily pad.
What is the least number of moves required in total for all the frogs to arrange themselves in the following configuration?
by
Agnishom Chattopadhyay
Are you sure you want to view the solution?
A ball of mass \(m\) is dropped from some height in a (uniform) gravitational field of \(g\). It reaches the ground and bounces directly upward, to 70% of its original height. During the bounce, the ball is in contact with the ground for a small, non-zero time interval of \(\delta t\).
What can be said about the normal force between the ball and ground during the interval \(\delta t?\)
by
Arjen Vreugdenhil
Are you sure you want to view the solution?
This resistive network forms an infinite binary tree--every branch splits into two new branches, where the new branch that goes to the left has a resistance of \(R_x\), and the one that goes to the right has a resistance of \(R_y\).
Suppose that after going down \(n\) levels, all of the branches are connected to a single node, \(B\). As \(n\) approaches infinity, what will be the equivalent resistance between nodes \(A\) and \(B?\)
by
Novak Radivojević
Are you sure you want to view the solution?
Consider the sum of the reciprocals of every positive integer that doesn't contain the digit 2:
\[\frac{1}{1} + \frac{1}{3} + \frac 14 + \cdots + \frac{1}{10} + \frac{1}{11} + \frac{1}{13} +\cdots+ \frac{1}{19} + \frac{1}{30} + \frac 1{31} \cdots.\]
Does this sum converge?
by
Efren Medallo
Are you sure you want to view the solution?