16 Aug 2013

Prize Maths Quiz: Tablet Access Codes (PMQ32)


Alice has a new tablet computer. At the login screen, rather than having to input a password, there is a grid of nine points. The login access code is created by dragging your finger from one point to the next in a predefined sequence. You may start at any point and drag your finger to any other point that can be reached directly by a straight line (without going through any intermediate points). You may not use the same point twice.

Assuming that Alice’s access code uses just 4 points (and 3 paths), how many such access codes are possible?

One example is given in the diagram. Also, just to clarify, a direct path between two points is one that does not intersect any other points. So, for example, one cannot go directly from the top-left point to the top-right point; in this case one must pass through the middle-top point. You can do it, but it will count as a 3-points and 2-paths route.

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.

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How to Enter

IF YOU ARE A STUDENT, you may still send your complete solution by email to pmq32cayley@giftedmaths.comThis email address shall be removed after the competition closes to avoid spam. This PMQ32 competition closes on WEDNESDAY 21 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.
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Enjoy the challenge!
Send us your solution! You can't win if you don't participate.


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