Problem Solving In GCSE Mathematics

My new book Problem Solving In GCSE Mathematics is now available at Amazon UK, Amazon.com and other Amazon sites.

Problem Solving in GCSE Mathematics Front Cover

It is a self-contained workbook, full of challenging problems covering the most demanding parts of the syllabus, with full solutions included.

It should be useful for anyone looking to achieve a top grade at GCSE or IGCSE.

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A little bit of magic

I first came across this problem years ago, somewhere online, but the exact source remains elusive:

Split \{1, 2, 3, ..., 2n\} randomly into two subsets X and Y, each containing n integers. Put the elements of X into increasing order x_1<x_2<\cdots <x_n and put the elements of Y into decreasing order y_1>y_2>\cdots >y_n

Prove that \lvert x_1-y_1\rvert +\lvert x_2-y_2\rvert + \cdots +\lvert x_n-y_n\rvert=n^2

Solution

Five People

Here is a problem that appeared in a Maths Battle in London a couple of weeks ago:

Donald, Jack, Peter, Richard and Steven have, in some order, the surnames Donaldson, Jackson, Peterson, Richardson and Stevenson. Donald is 1 year older than Donaldson, Jack is 2 years older than Jackson, Peter is 3 years older than Peterson, and Richard is 4 years older than Richardson. Who out of Steven and Stevenson is older, and by how much?

Solution