In these problems, which we learnt about from Maths Pickle, you will see some shapes made out of hexagons.
It might look something like one of these:
And we’re basically going to try to fill in each of the hexagons in one of three colours (red, orange or green).
Green means that from the starting point you can ALWAYS pass through all the hexagons (no matter what path you take). You can’t go back on yourself though.
Orange means that SOMETIMES you can pass through all the hexagons and other times you can’t (it depends on the path you take)
Red means that you can NEVER pass through all of the hexagons no matter what path you take.
Let’s look at an example:
Take this shape here:
If we start from the this hexagon:
We have two options of paths:
As you can see both paths pass through all the hexagons.
This means the top square is green:
Taking the same example. But starting from this hexagon:
There are 4 options of paths to take:
None of these paths pass through all the hexagons.
So the hexagon is red.
Finally if we start from this hexagon:
We have 3 options of paths:
Here some of the paths pass through all the hexagons and others don’t.
This means the hexagon is orange.
For the moment our shape looks like ths:
We want to fill each hexagon in in either red, orange or green.
Now try some of these ones to test your understanding!
Example 1:
Example 2:
Example 3:
Example 4: