Forgot password? New user? Sign up
Existing user? Log in
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 line segments shown divide parallelogram ABCD into 8 regions, and the areas of the orange triangles are 48, 21, and 63.
What is the area of the blue triangle?
by
Markus Michelmann
Are you sure you want to view the solution?
The weight of this hourglass is monitored constantly.
The last grain of sand falls from the top of the hourglass at t1, and hits the bottom at t2.
Which line best represents the readout of the weight on the scale?
by
Laszlo Mihaly
Are you sure you want to view the solution?
Is there a positive integer divisible by 2018 which only consists of the digits 3 and 0 (in base 10)?
by
Mustafa Alelg
Are you sure you want to view the solution?
If one of the two series below is equal to 2, what is the value of the other one?
⎩⎪⎨⎪⎧1+x+x2+x3+⋯x+2x2+3x3+4x4+⋯
by
Pi Han Goh
Are you sure you want to view the solution?
Your friend, David Hilbert, runs a casino with space for an infinite number of guests. He installs a slot machine with the following properties:
- Each guest at the casino plays one round at the slot machine after all the guests have arrived.
- If there are n guests at the casino, then the odds of winning the slot machine are always n1 for all of them.
- When a guest wins, they get all of the money in the machine.
To understand how profitable this machine is, he wants to know the probability that no one wins the slot machine.
If David fills up his casino with a number of guests approaching infinity, what does this probability approach?
by
Blan Morrison
Are you sure you want to view the solution?