23 Aug 2013

Prize Maths Quiz: Another Unfair Pizza Puzzle (PMQ33)

After a week of slicing up cakes and pizzas, here’s a PMQ with a similar theme.

Take a circle and randomly draw three distinct diameters, thereby partitioning the circle into six sectors. What is the probability that two of the sectors each has an area that is at least a quarter of the circle?

Just a note, that you may pick any random method, e.g., a random number generator for the angle of a diameter with respect to some zero point. Depending on your chosen method, you may end up with either a discrete or continuous function; it will be interesting to see how their results differ, and I shall accept both versions. You may, of course, come up with an altogether different method!

Have fun!

IMPORTANT CHANGES TO THE PRIZE MATHS QUIZ!

YOU MAY NOW DISCUSS THIS PMQ PROBLEM IN THE COMMENTS BELOW AND GIVE YOUR ANSWERS AND SOLUTION METHOD.

I SHALL POST A GUIDED SOLUTION ON THE FOLLOWING FRIDAY AT THE SAME TIME AS THE NEW PMQ. AS THERE ARE OFTEN MULTIPLE WAYS OF ARRIVING AT THE SAME ANSWER, I SHALL ALSO GIVE CREDIT AND LINK TO THE BEST ANSWERS SUBMITTED IN THE COMMENTS.

IF YOU ARE A STUDENT INTERESTED IN THE PRIZE BELOW, THEN YOU MAY STILL SUBMIT YOUR ANSWER BY EMAIL. BUT, FROM NOW ON, ONLY ELIGIBLE STUDENTS, PLEASE.

I HOPE THIS WILL MAKE THE COMMENTS MORE VIBRANT!

If you would like to DONATE PRIZES for the next PMQ, send me a message here.

How to Enter

IF YOU ARE A STUDENT, you may still send your complete solution by email to pmq33bernoulli@giftedmaths.comThis email address shall be removed after the competition closes to avoid spam. This PMQ33 competition closes on WEDNESDAY 28 AUGUST at 23:59 GMT.

The Prize

The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

Quick Rules

Look at the expanded rules on our PMQ page.
Anybody can enter our Prize Maths Quiz; adults and students.
Use the official server clock in the right column to avoid late entries.
All emails and email addresses sent to us will be deleted after the winners have been processed.
DO NOT submit your entries to the comments section at the bottom of this post.
You CAN discuss it there but you must email us to enter the competition.
We adhere to COPPA guidelines regarding children's online safety and security.
Enjoy the challenge!
Send us your solution! You can't win if you don't participate.