Domino Triangles: Winner of PMQ20: Middle Secondary Mathematics

Before launching into the question itself, note that this question was the winner of PMQ20, where you were asked to design your own question based around dominoes. A big “Thank You” to Chris Breederveld for submitting the puzzle below.

The Question

Take one full set of dominoes and remove those tiles with blanks, leaving you with 21 distinct tiles. Orient each tile vertically so that it denotes a rational number. For example, the tile [5/2] can be used as the fraction 5/2 or as 2/5. The aim is to arrange six tiles into a triangular grid in such a way that a tile-fraction is the sum of the two tile-fractions immediately below it.

Given that the tile at the top of the triangle is [6/6], how many solutions can you find? Treat reflections as one unique solution.

The diagram below shows the start of one possible solution. Note that the only restriction is that the [6/6] must be at the top.

Winners of PMQ16 and PMQ17

My apologies for being a little lax with these announcements. I'm often waiting for replies and then it slips down the list of things to do. My excuse is that sometimes the questions take a long time to compose! This weekend, I shall be resending emails and hopefully come right up to date.

One thing to remind everyone who has sent in a PMQ answer. You will immediately receive an automated reply; this is done so that you know that your email has been received and not to send another one! Also, when you see this, please add the domain to your white list so that the prize winners announcement doesn't get caught in whatever spam trap you may have.

OK, without any further rambling...

PMQ16 Winners

Jeffrey Bond from the USA
M.K.

These were the only two entries that had at least one of the questions correct. If you wish to try the question, then just go to PMQ16 - but be careful as the answers are in the comments section!

PMQ17 Winners

Chris Breederveld from The Netherlands
Tan Qi Huan from Malaysia

You can try the question at PMQ17. Be careful, the most common mistake in this puzzle was to forget that there is an even prime!

Congratulations to all the winners and thanks to everyone who participated.

If any of the above winners wishes to add a link to their personal page such as G+ or Facebook, then please get in touch or send me a PM within G+. Thanks.

Prize Maths Quiz: Winners of PMQ8!

We seem to be inching forward with just one winner per week. Never mind, the site and its social networks continue to grow so I shouldn't be too concerned.

Also, many of our members interact in our Mathematics Competitions Google+ community rather than on this website. Again, never mind, but it makes this site look unloved!

We don't have a strong presence on Facebook, so if you're on Facebook, help us out by sharing our posts and liking our page. Better still, join us on Google+!

Enough chit-chat, our Winner of PMQ8 is:

D. W. (Singapore)

Congratulations! An email has already been sent.

Next competition is PMQ9 starting Friday 8 March at 02:11 GMT.

See you Friday!

Prize Maths Quiz: Winners of PMQ7!

The latest PMQ, Five Circles in a Triangle, probably had the longest solution so far, involving both geometry and a bit of number theory. Once again, like last week, we have only one Winner.

Congratulations go to:

G. McR.

An email has been sent and I look forward to welcoming a new member into our online mathematics club.

The next competition, PMQ8, will start on Friday.



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Prize Maths Quiz: Winners of PMQ6!

PMQ6, the Tricky Tower, has been our most popular quiz question so far, a least in terms of traffic to the page. However, there was only one correct answer submitted.

Congratulations go to:

J.Y. (from the UK)

I will post the answer to the problem later this week, but there is a discussion on-going at our Mathematics Competitions Community on Google Plus. Unlike the standard Tower of Hanoi, colouring the discs creates some limitations in the possible moves. It also destroys the simple formulas that are associated with the standard puzzle.

This could form the basis for an interesting project. Start with a 2-colour Tower of Hanoi, with alternating colours, and see whether you can find a pattern such that you can calculate the number of moves needed to solve a 100-disc tower!

More on this coming soon...



Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. Shorter questions posted on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.

Prize Maths Quiz: Winners of PMQ5

Thank you to everyone who submitted their answer to PMQ5 (Mercury and the Sum of a Series).

Before I announce the winners, I need to mention a slight change to how I do this from now on. I used to wait for the winners to respond to my congratulatory email so that I could list their names and countries. However, some don't bother replying, so that it looks as if nobody won! So, from now on, I shall announce the winners using just their initials or part of their email address. Then, once the winners have responded and the actual claimant student has accepted the prize, I will list the names as they join our online classroom.

Having got that out of the way, this week's winners are:

K.R.
M.K.
J.K.

An email has already been sent.

For the first time, we have had more submissions than prizes, so to those who didn't win this week, please try again next Friday.

Well done!

Richard
GiftedMathematics.com

Prize Maths Quiz: Winners of PMQ2

Again, we had very few entries to our PMQ2 Ice-creams and Cubes competition. However, there were more for PMQ3, so I'm glad to see participation picking up. I will announce the PMQ3 winners once they have replied to my email.

back to PMQ2, I am pleased to announce that our one and only winner is:

Andrew Grounds (USA)

Well done!

PMQ4 will be posted this Friday and I shall announce the exact time during Thursday.

Please make sure you read our full rules on PMQ events and our committment to COPPA guidelines regarding children's online security.

See you Friday!


Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter.

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.