Maths item of the month
May 2013
The two colour theorem?
Given n circles in the plane, prove that no matter how these circles are arranged, the map which they form may be properly coloured with two colours.
This problem is taken from a 2012 MEI Conference session. For details of the 2013 MEI conference see: www.conference.mei.org.uk.
April 2013
April fool: 2+2=5
Can you spot the mistake in the following "proof" that 2+2=5?
March 2013
Next factor
Starting with the number 2, integers are added, in order, as vertices to a graph so that any two vertices are joined if one of them is a factor of the other. A graph for {2,3,4,5,6} is shown.
What is the maximum integer that can be reached if none of the edges of the graph are allowed to cross?
This is a version of the nrich problem Factors and Multiples Graphs.
For more problems see the nrich website.
February 2013
Squaring the circle
In the diagram below the circle and square have the same centre and the same perimeter.
What fraction of the area of square lies outside the circle?
What fraction of the area of circle lies outside the square?
January 2013
Trying Triangulars
The triangular numbers are 1, 3, 6, 10, ...
17 can be expressed as the sum of distinct triangular numbers:
17 = 1 + 6 + 10.
5 cannot be expressed as the sum of distinct triangular numbers.
What is the largest positive integer that cannot be expressed as the sum of distinct triangular numbers?
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