# Maths Training

There are several different maths puzzles on offer at this site and Speed Maths for you to practice.

This question requires you to read through the scenario, and then answer the questions that follow. You may find this easy or difficult depending on your mathematical abilities and confidence. If you find any part difficult, try writing down different combinations that you can come up with, or even all possible combinations, in order to find the answers.

**The Dance**

In the local dance competition, the judges award each contestant a mark, and this is turned into points at the end. Each contestant ends up getting awarded between 1 - 10, and each mark is awarded exactly once. There are ten contestants.

The audience then votes independently at the end, and these votes then get translated into an additional mark of between 1 and 10 getting added to the judges score for each contestant. The same rule follows - each number from 1 to 10 is awarded to exactly one contestant. The end result is that the two contestants with the lowest score enter a 'dance off' and the judges then ultimately decide which one goes.

**The Questions**

a) What is the maximum score a contestant can get?

b) What is the minimum score a contestant can get?

c) Can the team who finish top with the judges end up in the bottom two after the public vote has been taken into account, assuming priority is given to the public vote over the judges vote? Is it even possible for the top two with the judges to end up in the bottom two overall?

**The Answers**

Once you have written down your answers, then check them against the below and see if you got it right:

a) 20

b) 2

c) Yes. For instance if the public rank the contestants in the reverse order done by the judges, all contestants end up with 11 points. As the public rank takes precedence, the top two with the judges end up as the bottom two.