List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
How to build your own magic squares.
Weekly Problem 2 - 2013
After performing some operations, what number is your answer always a multiple of?
This is then covered with a layer of blue cubes.
How many red cubes have you used?
How many blue cubes have you used?
Find an easy way of working this out.
Now imagine adding a layer of green cubes.
How many green cubes are needed?
Have you a quick method for working out the amounts that you
would need for each layer?
Martha thought about the third
layer like this:
Can you see it like this?
Using this method, if you have an $x$ by $x$ by $x$ cube, can
you explain how to find an expression for the number of cubes
needed to make the next layer?
Emma made the third layer like
[You may like to view this animation
- but at 700kb it is quite large and will take 2 to 3 minutes to
download unless you have a broadband connection]
Charlie made the third layer like
Can you show that all three
expressions are equivalent?
Can you find another way to think about this problem?
Show how you form your expression, and show that it is
equivalent to the examples above.