Today is 28 January 2020, the 28th day of the year.



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Sally Simplewit is a great observer of human nature and the social scene, especially in her college dormitory. In particular, she has been keeping track of all the cliques and friendship groups. Everybody in her dorm seems to have at least one friend, and some have a great many friends. Some, she notices, have an even number of friends, and some have an odd number of friends. Oddly, the number of people with an even number of friends is sometimes odd, but the number of people with an odd number of friends is always even. As a scientist-in-training, Sally is curious to know if this is just an oddity, or if it always works out that way. Unfortunately, none of her friends in the other dorms seems interested in helping her by counting friendships in their own dorm. Odd.
Today's challenge: Can you help Sally prove whether or not the number of people with an odd number of friendships in any given group is always even?


Solution to yesterday's challenge

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