Today is 28 January 2015, 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? HINT Solution to yesterday's challenge THE MATH STORE LIVES! At last, the new Math Store is open, including all the downloads we have offered in the past. Please come poke around the shop and let us know what you think! NEW FOR 2012: Platonic Realms is at last being rewritten and moved to a new server. Please check back soon to see the new look, new content (together with all your old favorites), and an all new math store! This site is registered with the Internet Content Rating Association (ICRA), and is suitable for all ages. Because we value freedom of expression on the internet as well as the privacy and comfort of our visitors, Platonic Realms is also bug-free and blink-free. Platonic Realms uses cookies for site-traffic analysis, but these automatically expire soon after your visit. Our privacy policy is very simple: we ALWAYS ask our visitors before collecting any personal information, and we NEVER share information about our visitors with anyone else. Period.

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