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Follow the Numbers

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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Journeys in Numberland

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Factor Track

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Factor Track is not a race but a game of skill.
Below is a simple training version. The idea is to go round the track in as few moves as possible, keeping to the rules.

You start on the (yellow) $60$ and must make your way round to the (red) 'end' square.
You can move any factor of the number you are on, except $1$.
You must land exactly on each green square, so you can't go round corners in one move.
Have a go at moving round this 'training' track following the rules.  
Can you do it in fewer moves?

When you feel ready, try this more complicated track where there are possible short cuts. You will have to work out whether they are worthwhile.
 bigger track

You might find it easier to print out this larger copy of the track which also has the rules on it.

You can do this on your own or with a friend. Who can get round in the least number of moves?

What is the best route to take to do it in the least number of moves?
Which squares do you need to land on?

Printable NRICH Roadshow resource.