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
\[ \begin{array} { rrrr }
& & A & B & C \\
& & B & C & A \\
&+ & C & A & B \\
\hline
& & &\phantom0 &
\end{array} \]
In the cryptogram above, \(A,B,\) and \(C\) are each single-digit integers that are not necessarily all distinct. Which of the following is a possible value of the final sum?
by
Christopher Boo
Are you sure you want to view the solution?
The hexagon below is regular. Which of the two colored areas is larger?
by
Agnishom Chattopadhyay
Are you sure you want to view the solution?
A ceiling fan is hung on a hook through a spring balance, which reads \(M\) kg when the fan is off.
If the fan is switched on and rotates at a constant speed, then what will be the reading on the balance?
\(\)
Details and Assumptions:
- Ignore the effects of torque.
- The fan blows the air downwards.
by
Rohit Gupta
Are you sure you want to view the solution?
You are offered two cupcakes. One is poisoned and the other is safe to eat.
You happen to be in a village full of knights (who always tell the truth) and knaves (who always lie), but you can't tell which is which by their appearance.
You ask one of them, "Which cupcake is safe to eat?" To this he makes the following two statements,
1 2 | |
Which cupcake is safe to eat?
Assumption: The person you ask knows which cupcake is which.
by
Geoff Pilling
Are you sure you want to view the solution?
\(\)
The above is one possible way to arrange 5 unit squares into a polygon, and this polygon has a perimeter of 12. What is the minimum possible perimeter of a polygon that can be constructed with 5 unit squares?
\(\)
Details and Assumptions:
- No overlapping is allowed.
- A vertex can only touch a vertex--not anywhere on the side--of other squares.
by
Christopher Boo
Are you sure you want to view the solution?