11 Jan 2013

Prize Maths Question: The Game of 24 (PMQ1)

Adrien-Marie Legendre, died 180 years ago 10th January 1833
"Every Friday, I get that PMQ feeling." Legendre
Miss Abel likes to set a quick brainteaser at the start of her maths lessons. The students love it and it gets them in the right frame of mind for the rest of the lesson.

Today she wrote on the board:

Sum to 24

a) 4 5 6 7

b) 5 5 5 5

c) 3 3 8 8

The students had played this game many times before so had no need for the rules. For those of you who haven't, the rules are very simple.

Using all the four single-digit numbers, in any order, make a total of 24 using only the four arithmetical operations and brackets if you need them. No other symbols or numbers are allowed.

It usually takes less than 5 minutes for some of the bright sparks to do all three sums, but on this particular day Miss Abel could see many of her students frowning. "Why was it taking them so long?" she thought.

Finally, Alice put her hand up. "Miss, I can get 25 but not 24. It's impossible!" A murmur of agreement rippled through the class.

Miss Abel was certain she hadn't set anything that hard. She took a quick look at her notes, then looked at the board, then back at her notes, and... she'd written one of the numbers wrongly! She quickly tried to do the sum in her head and, just like Alice, could easily get 25 but not 24. The 5-minute puzzle had turned into a 15-minute challenge.

"I'm surprised nobody has managed to do all of them, so I will leave this with you as a homework puzzle. Right, today's lesson is about..."

Can you do better than Miss Abel and her class? Find all three sums to 24.

The Question

Solve the above problems (a), (b) and (c).

You must include your answer to all three problems in acceptable algebraic format, for example, (3+5)*6/2.

You must submit your answer to the email address below.

Eligibility to Enter

This Prize Maths Question can be entered by students in Primary, Lower Secondary or Upper Secondary school. Basically, anybody 16 years or under can participate. However, if you are under 13 years old and win a prize, we shall require parental approval to join our Online Classroom. Please note that the aim of this website is to help school students master the topics found in school mathematics competitions and challenges. Everyone is welcome to use our free online activities but the Online Classrooms are only for genuine students of school age and not for older students or adults interested in maths games and puzzles. You can go to our Mathematics Competitions Community and participate there.

The Prize

This week's prize is a free place in our Online Classroom for 2 months.

This prize will be awarded to the first correct entry submitted plus four more lucky winners will be selected at random from all other entries. The selection shall be random but weighted towards the quickest replies. This PMQ will close after 24 hours. As this is the first PMQ, it may remain open beyond 24 hours until there are enough winning entries.

Submissions will only be accepted by an email sent to [Competition closed. Email address removed. Feel free to discuss this in the comments below.] DO NOT submit it in the Disqus comments box below. You may discuss the question on Disqus but it will not count as a competition entry. All attempts to send multiple answers or any other form of cheating will result in all such answers being deleted and no prizes being awarded to any such participants, including the original. If you want to guarantee that your email has been sent then just CC it to yourself and check that you have received a copy back. The timestamp on the emails will determine the winners. The above email will be disabled once this PMQ competition has been completed.

Winners will first be notified by email. Once all winners have shown they are genuine students, they shall be announced on this website.

Good Luck!

And once you've submitted your entry, tell your friends about this PMQ!

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