18 Jan 2013

Prize Maths Quiz: Ice-creams and Cubes (PMQ2)

"Hey, Brenda, finish that PMQ later. Come and look at this!"
Alice and Brenda had spent the day at a flea-market helping their parents sell some old stuff. They were both able to keep the money they made from their own old toys and books. They agreed to meet at a local ice-cream parlour to relax and count their takings. But on arriving, Alice could see her friend had been crying.

"What's wrong Brenda? Why are you crying?"

"Look!" Brenda pointed to her little money box. "Empty! All the money I made today has gone! I don't know what happened, I couldn't just have lost it. My whole day wasted, and can't even buy some new books!"

Alice quickly added up the few coins left in Brenda's money box. She had already counted hers to the nearest penny. Being a bit of a maths whizz, Alice did a quick calculation and said to herself, "Mmm... that's bizarre, my money is exactly the cube of yours; in pennies, of course."

This made Brenda feel even worse, and the poor girl started crying again.

"Look, if we add them up the total comes to a whole pound and I can give you a quarter of our combined total. Then I will only have three times your money. How does that sound?"

Brenda was speechless. "You'd do that for me?"

"Yes, no problem." beamed Alice. "Isn't that what friends are for?! Come, let's order. Now you have some money, ice-creams are on you!" They both laughed.

The Question

Counting their money in pennies, Alice's number is the cube of Brenda's. Added together their total comes to an exact whole pound amount. Alice then gives Brenda a quarter of this total. What is the smallest possible total that satisfies these conditions, and how much money is Alice left with?

Your answer must include both numbers.

[ 1 pound = 100 pennies ]

How to Enter

Send your complete solution by email to [PMQ2 closed: email removed. Feel free to discuss this in the comments below.]. This email address shall be removed after the competition closes to avoid spam. This PMQ2 competition closes on Sunday 20 January at 23:59 GMT. Please look at the official server clock in the right column to avoid late entries. All emails and email addresses will be deleted after the winners have been processed; please read below for details. 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.

The Prize

The prizes for this PMQ2 are 5 free places in our Online Classroom for 2 months. The very first correct solution will receive a prize plus four others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received.

Note that the randomly selected winners are weighted towards the quickest solutions. So, submit your answer and then tell all your friends!

Eligibility: Who Can Enter?

Anybody can now enter our Prize Maths Quizzes; students and adults. The actual prize remains the same and we shall send the winners an e-voucher that can be used by any student who is under about 16 years old and studying or aiming to enter a mathematics competition.

How Does the e-Voucher Work?

The winners are sent an e-voucher by email. They can use it for themselves (if they are students), their child or student. Follow the instructions in the e-voucher and send it back to us once you have decided who will take up their place in our Online Classroom. We then send back a form to be filled in by either a parent or teacher of the nominated student. This is in compliance with COPPA regulations so that we have the consent of an adult. Once we get that form back we will issue you with an access code to our classroom on Edmodo. The student can then create an account and is automatically added to our Online Classroom. Once the student has created an account, a parent can then also create a connected account on Edmodo to monitor the student's progress. This may sound complicated when written down but could all take no longer than a couple of hours or a couple of days, depending on time zones.

And Finally...

Please notice that in all this process the only thing that we at Gifted Mathematics need is one valid adult contact email address. Again, this is for the security of the students and compliant with COPPA regulations.

Please also note that all other email address that enter our competition are deleted once the winners are announced and e-Vouchers distributed. We do not keep them for future mailings because it is impossible to tell whether an email address belongs to an adult or a child. This too is part of our commitment to COPPA and to creating a safe and enjoyable learning environment for students.

If you have any questions, please leave a comment below.

Enjoy the challenge!


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