skip to content

STEP Support Programme

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.

Assignment PDF: 
Hints and Partial Solutions: 

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)