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'Nineteen Hexagons' printed from https://nrich.maths.org/
Why do this problem?
This problem is a good way for children to gain familiarity with multiples of two and five. In addition, it encourages a systematic approach to problem solving by asking for all the possible routes.
It might be useful for children to mark all the multiples of two and five on a number line or number square before they start on the maze.
This sheet gives a number of small copies of the maze for rough working and recording the various routes.
This blank grid may be useful for pupils to make their own
mazes.
Key questions
Have you marked all the multiples of two and five on your number line/ number square?
Would it be a good idea to circle all the multiples of two in red and all the multiples of five in blue to start with?
Can you see an even number/multiple of two?
How can you tell that a number is a multiple of five/in the five times table?
Where can you go from here?
How many ways have you found so far? Can you see any other ways?
How are you going to record your paths so you know where you've been?
Possible extension
Children could be given cards with numbers $1$ to $20$ and challenged to find all the possible ways that a multiple of two followed by a multiple of five could be selected.
Possible support
Suggest using a number line or number square for marking all the multiples of two and five before tackling the maze itself. Then start on the maze by circling all the multiples of two in one colour and all the multiples of five in another colour.