## 25 Jan 2013

### Prize Maths Quiz: Tinkering With Triangles (PMQ3)

Alice was sitting on the floor toying with her number cards. She was using them to make pretty shapes and then see if she could make number patterns with the shapes.

Her attention was suddenly distracted by a clatter behind her. “What are you doing?” Bill looked like he was in the middle of destroying her torch; though more likely nearer the end.

“Sorry, I was just taking it apart to see how it works.”

“Huh?! There are no moving parts in a torch. Is that your big discovery?”

“Ah, but there is... there's the switch!”

“And what good is a torch without a switch?” Alice stood up and leered down at Bill, who seemed to have surrounded himself with an octopus’s garden made from bits of her torch; her ex-torch. Actually, it was also her lost torch; where had he found it?

“It wasn’t working, so I looked inside and, with a bit of force I bent this little switch here so that it now touches the battery. I’ll show you once I put it all together.”

If you put it back together!” snapped Alice. She looked at Bill with a puzzled stare; she was searching for something in her mind. Tinkering! That’s the word, Alice thought. She went back to her numbers, with the idea in her head that perhaps Bill wasn’t always such a pea-brain. Then again, he might just be pretending to be clever by breaking things.

She flopped herself back down on her big cushion and surveyed the numbers scattered around her. Perhaps this was her garden and perhaps she too was a tinker. Time to put some order into this chaos.

Now let me think...

The Question

Place the numbers 1 to 9 into the triangular grid (shown above) in such a way that the sum along each side equals 21. You must use every number.

a)    What is the sum of the three corners?

b)    Find a complete solution and show your method of solution.

You may give your final answer either as three rows of four digits, each starting at a vertex, or a string of numbers starting at any vertex and going around the triangle.

How to Enter

Send your complete solution by email to [Email removed. Competition now closed. PMQ4 starts next Friday]. This email address shall be removed after the competition closes to avoid spam. This PMQ3 competition closes on Sunday 27 January at 23:59 GMT.

The Prize

The prizes for this PMQ3 are 4 free places in our Online Classroom for 2 months. The very first correct solution will receive a prize plus three others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received.

Quick Rules

Look at the expanded rules on our PMQ page.
Anybody can enter our Prize Maths Quiz; adults and students.
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