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Students could also watch "Bridges of Königsberg: The Movie"!
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?