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Euler used a graph to explain the possible routes around Old Konisberg. He represented the land by dots and the bridges by lines joining the dots. Think about whether there is an even number of bridges or an odd number of bridges from each piece of land.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?