## 14 Sept 2013

### Prize Maths Quiz: Intersecting Chords Game (PMQ36)

Imagine a circle with six distinct points marked on its circumference and labelled 1 to 6. There are also six cards numbered 1 to 6. The cards are shuffled and placed face down on a table. You pick two cards and look at the numbers on them; join the two points shown on the cards by a straight-line chord. You then pick two more cards and join those two points with a chord. Finally, a chord is drawn joining the last remaining pair of points.

You win the game if none of the chords intersect. What is the probability of winning this game?

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 HOPE THIS WILL MAKE THE COMMENTS MORE VIBRANT!

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How to Enter

IF YOU ARE A STUDENT, you may still send your complete solution by email to pmq33bernoulli@giftedmaths.com.[note that this email still works] This email address shall be removed after the competition closes to avoid spam. This PMQ36 competition closes on WEDNESDAY 18 SEPTEMBER 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.
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Enjoy the challenge!
Send us your solution! You can't win if you don't participate.