Submit your own mathematics competition question!
During the past week, I have mentioned a couple of times that I would be trying this as an experiment. I would like you to submit a question that could possibly be found within a mathematics competition. The question must involve dominoes as part of the problem. The actual branch of mathematics could be anything, such as combinatorics, sequences, fractions, geometry or anything else you can think of. However, the construction of the problem must involve some manipulation of dominoes. Examples can be found here, here and here.
You must submit your original question in full plus the answer and solution. As it usually takes longer to devise a question than to solve it, just for this week I have extended the deadline to Thursday night. It will also take me longer to read through the submissions rather than just checking that the answers are correct. The best questions will be published on this website, with due acknowledgement and a link to your personal homepage. I reserve the right to edit the questions for language, so if English is not your first language, don’t worry, I shall correct any grammatical errors; the idea is more important than the precise wording. If your question involves a diagram, then submit it as an attachment or include a link to the URL of the image. However, I expect each question to be your original work. Each individual may submit a maximum of two questions; if I see too many from the same email address I shall delete unread any further submissions beyond the two - so pick your best.
Your question should also be solvable with just pen, paper and brain, without any electronic calculating device. It should also be solvable within a reasonable time, assuming it is in a proper test paper, so a maximum of 10 minutes for a really hard question. I know it is difficult to estimate solution time, but if you try the same question yourself and time it, then multiply this by a factor of 3 for extra thinking time.
If I have missed out anything, or you wish to clarify any points, please leave a comment below.
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How to Enter
Send your complete solution by email to firstname.lastname@example.org. This email address shall be removed after the competition closes to avoid spam. This PMQ20 competition closes on
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.
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.
Then tell your friends!