AIMSSEC Puzzles
Links to selections of puzzles for different age groups:
Learners age 8 to 12
Learners age 12 to 15
Learners age 16 and over
March 2010 Farey Sequences
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If I gave you a list of decimals, you might find it easy to put them in order of size.
But what about ordering fractions?
A man called John Farey investigated sequences of fractions in order of size - they are called Farey Sequences.
The third Farey sequence is shown here.
The third Farey sequence lists in order in their simplest form, all the fractions between 0 and 1 which have denominators 1, 2 and 3.
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The fourth Farey sequence is shown here.
The fourth Farey sequence lists in order in their simplest form, all the fractions between 0 and 1 which have denominators 1, 2, 3 and 4.
Can you find the fifth Farey sequence? |
February 2010 Legs Eleven
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Take any four-digit number, move the first digit to the 'back of the queue' and move the rest along.
For example 5238 would become 2385.
Now add your two numbers.
Is the answer always a multiple of 11? Can you prove it?
What happens when you do this with three-digit numbers? Five-digit numbers? Six-digit numbers? 38-digit numbers ... ?
Prove your findings! |
January 2010 The answer is 2010, what is the question?
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You could try things like:
2000+10 or 201 x 10 or 500+1000+500+5+5
or even
See what different questions you can find and compare yours with others.
Perhaps you can make up one that is easy,
one that is harder and one that is very hard.
Don't forget you might like to use calculators or computers! |
This webpage has a new problem each month. Solutions are invited from individual learners or groups
or you can even send one solution from your whole class. If you send us a good solution it will be published
on this webpage. Send your solutions by email to
aimssec@aims.ac.za or by post to AIMSSEC 6 Melrose Rd, Muizenberg, 7945, Western Cape giving the name(s)
and age(s) of the learners and the name of your school.
The puzzles come from the NRICH website where you will find
hundreds more problems with solutions from learners sent in from all over the world.
There are also notes for teachers about using the problems in their lessons.
There are problems at different content levels and different challenge levels suitable for every age group.
Some of the problems have interactivities and to be able to use them you need Flash on your computer.
Flash is entirely free and to download it to your computer see
the Macromedia website.
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