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
The two watering cans above have equal base areas. Their spouts are both open. Which of the two cans can hold a greater volume of water in equilibrium in the upright positions as shown above?
by
Deva Craig
Are you sure you want to view the solution?
You reach a fork in a road: one path leads to Truth City while the other leads to Lies City.
You encounter a man who you know is either from Truth City or Lies City. If he is from Truth City, he will tell the truth, and if he from Lies City, he will lie.
What question will make him point to Truth City?
by
Terry Yu
Are you sure you want to view the solution?
\[ \begin{array} { rrrrr } & & & & & A \\ & & & & A & A \\ & & & A & A & A \\ + & & A & A & A & A \\ \hline & \large\square & \large\square & \large\square & \large\square & \large\square \\ \end{array} \]
The above is an incomplete cryptogram, where \(A\) is a positive, single-digit integer. As shown, the final sum is a 5-digit number.
What is this final sum?
by
Pi Han Goh
Are you sure you want to view the solution?
Bobo the Clown wants to cross a bridge over dangerous waters while performing a three ring juggle, in which one or two rings are in the air at all times. The bridge can support a maximum weight of \(\SI[per-mode=symbol]{1000}{\newton},\) above which it will collapse. Each ring weighs \(\SI[per-mode=symbol]{100}{\newton}\) and Bobo himself weighs \(\SI[per-mode=symbol]{800}{\newton}.\)
Coco the Clown tells Bobo that it will be safe to cross the bridge as long as Bobo is never holding all three rings at once. Dodo the Clown disagrees, arguing that the juggle will collapse the bridge, even if at least one ring is in the air at all times.
Who is correct, Coco or Dodo?
by
Deva Craig
Are you sure you want to view the solution?
We have a \(1\times 1\times 1\) orange cube on a piece of \(3\times 3\) blue paper. Is it possible to cover the entire cube with the paper under the following conditions?
- The paper can only be cut or folded along the grid.
- The cut should not cause the paper to separate into pieces.
by
Ronald Chén
Are you sure you want to view the solution?