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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

June 2010 Football Challenge

World Cup 2010 logo

FOOT
BALL +
GAME

Each letter represents a different digit.
How many solutions can you find? There are 224 altogether.

Example: F=2, O=9, T=7, B=3, A=4, L=1, G=6, M=0, E=8

2997
3411 +
6408

May 2010 Trisquares

L shape of 3 squares

These 'trisquares' are made up of three squares and each has an area of 3 square units.
Can you fit them together to make an enlargement of the shape? What is its area?
Can you fit trisquares together to make enlargements of scale factors 3, 4 and 5? What are their areas?
Is it possible to make enlargements of all sizes by fitting trisquares together?
Squared paper would be useful for working on this challenge.

April 2010 Painted Cube

Red cube and yellow paint

Imagine a large cube made up from 27 small red cubes.
Imagine dipping the large cube into a pot of yellow paint so the whole outer surface is covered, and then breaking the cube up into 27 small cubes.
How many of the small cubes will have yellow paint on their faces?
Will they all look the same?
How many red faces and how many yellow faces do they have?
Now imagine doing the same with other big cubes made up from small red cubes.
What can you say about the number of small cubes with yellow paint on?
What interesting discoveries can you make?

March 2010 Farey Sequences

Third Farey Sequence

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.

Fourth Farey Sequence

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

eleven legs

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?

blackboard

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.