STEP Support - Assignment 12
This STEP support module includes proving divisibility of some expressions, probability and a logic puzzle. Previous assignments can be found here, but you can do this one without having done the others first. STEP questions are difficult, they are supposed to be and you should expect to get stuck. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck").
About this assignment
The assignment is published as a pdf file below. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. Finally, there is a warm-down exercise. The warm up for this assignment asks you to show that $n(n+1)$ is always even when $n$ is a positive integer, and similar facts. The main STEP question (2011 STEP 1 Question 12) is about selling raffle tickets and the probability that there will be enough change for everyone. The final question seems to be unsolvable. Start by finding all the possible solutions and then use the information given in the question to work out what the actual solution is.
Further reading
For some advice on tackling probability questions and more problems to solve, see this NRICH Advanced Problem Solving module . The problem is the STEP question is equivalent (or nearly equivalent) to Bertrand's ballot theorem, where you are interested in the probability that one candidate stays ahead of the other throughout the voting process. For more on the mathematics of bell ringing, see this Plus article.
Hints, support and self evaluation
The “Hints and partial solutions for Assignment 12” file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers.
