Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
We often roll a die to find a number from $1$ to $6$ for a game
that we're playing. We wait until the die stops and then see what
number is on top. What about if we slow it down and have the die
slowing rolling along? What if we make it even slower and we move
the die to a new face one at a time?
In this way we can move the die forward/backward or right/left.
You might like to think about it as North, South, East or West.
When I first thought about this I thought of the die leaving a
kind of "footprint" of the bottom number wherever it went on its
journey. You can do this if you want to.
I then found it easier to look at the number on the top as each
new "step" was taken.
So with a die which might show:-
- or maybe you have one with numbers on it:-
we can go on a little journey:-
So, starting with $1$ on the top we move down. (I make sure that
$2$ is going to come up by moving the die around before
starting.) I then got $2$ followed by $6$. I then rolled it over to
the right a few times. $3$ shows up, then $1$ again,
followed by $4$.
Another journey could be:-
We start off as before. But, when I've rolled to the
right a couple of times, I go up and it shows a $2$, and then left
and it shows a $3$. It's a bit difficult to see where I've gone so
I've added an arrow to show the direction.
What I CANNOT do now it to go further by rolling left from that
last $3$ which would give a $5$ on top of the $2$ I had from my
first step. Remember - no crossing back again!
So, explore a little and see what things happen as you roll
around different paths and you write the numbers down.