The main Kintyre Way Relay is divided into 6 sections and you can enter a team of up to 6 runners (including the possibility of a team of 1, i.e. a solo runner doing the full 66 miles).

You can change runners at any of the intermediate checkpoints, but not anywhere else. For example, in a team of 2, runner A could do Tarbert – Claonaig and runner B would then do Claonaig – Campbeltown (unlikely though this might be).

For simplicity, assume that once you have handed over to another runner, you cannot then do another section later on. (But please note, this restriction does not apply in the real race)

Question 1

How many different possible combinations of team size and changeover points are there?
(The example above would count as one combination.)

Question 2

Having answered question 1, most likely by making a simple list of all the possibilities, can you come up with an elegant explanation and/or formula for the answer? Your solution should make it easy to calculate the number of possible combinations for a similar race with any number of sections (for example, 10 sections instead of the original 6).

Hint: a formula alone is not enough. You need an explanation to show why the formula works.

Send in your solution to question 2 along with your entry form, to reach us no later than 19th April 2008.

If you come up with a correct solution, your name will be entered into a prize draw to take place at the presentation in Tayinloan on 10th May. For details of prize, check the Latest News page.