Satnav dilemma
How many routes are there in this diagram from S to T?
Age
11 to 14
Challenge level
Problem
How many different routes are there from S to T which do not go through either of the points U and V more than once?
Image
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
There are 3 routes from S to U and 2 from U to V. The number of different routes from S to T is therefore 3 x 2 =6. Each of these can be followed by any one of three different routes from V to T, making a total of 6 x 3 = 18 routes in all.