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## 'Stairs' printed from http://nrich.maths.org/

Let's suppose that you are working in the school hall to help
with setting up the stage for a play or an assembly. Perhaps you've
got a stage that is raised up and there are some steps that lead up
to the stage. From the side the steps might look a bit like
this:-

These steps have been made up using blocks so that you go up a
total of 6 and along a total of 6. The steps could have been made
up another way:-

In this case the steps are not equal and some of them need you
to make a big step up. Well, that does not matter.

Have a go at drawing some other steps that would take you up 6
and along 6.

### My challenge to you today is to design different step
arrangements, with the following rules:-

You need to go along a distance of 6 on the steps, so this one
breaks the rule:-

You need to end up at 6 high. So this next one breaks the rule and
is not allowed:-

You cannot go DOWN once you have gone up. So this next one is not
allowed either:-

But, you can go along more than one block without going UP like
this one:-

As a little extra, you may have noticed that you can count how
many square blocks have been used for each design.

The very first example above used 21 and the last one used 33
square blocks.

Here are some questions you might like to think about to do with
the number of square blocks used:-

- What is the largest number of square blocks that can be
used?
- What is the smallest number of square blocks that can be
used?
- Can you get to use all the numbers that go between your answer
to a. and your answer to b. ?

Then :-

I wonder what would happen if it were
4 along and 4 up?

I wonder what would happen if it were
5 along and 5 up?

I wonder what would happen if it were
5 along and 6 up?

I wonder what would happen if it were
6 along and 5 up?

I wonder what would happen if
...?

Please send in your solutions and comments.