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Bard Math Circle Day 0

It’s the day before Bard Math CAMP, and our resident mathematicians have been busy getting ready for arrival day. The 0’s need to be properly inflated, our curly bracket’s (For our Computer Science minions) must be gone over with a curling iron, and our Greek letter’s must be taken out, sorted, and thoroughly dusted. Despite the work, everyone prepping for Bard Math CAMP has had some time to do their daily regimen of mathematical exercise.In fact one of our mathematicians noticed something interesting about the number of campers arriving tomorrow. While we were celebrating the birthday of Bartholomeo Pitiscus, the mathematician who coined the word “Trigonometry”, a resident mathematician decided to calculate the probability of at least 2 of our 23 campers sharing the same birthday. Try the problem out for yourself! Is the result what you had expected?Another of our mathematicians made this logic puzzle after observing the areas where our mathematicians come from.We have 23 mathematicians coming from Arlington, Bethlehem, Brewster, Catskill, Hyde Park, Kingston, New York City, Onteora, Red Hook, and Rhinebeck. Six areas have exactly one mathematician. Rhinebeck has one quarter the number of mathematicians that Kingston has, and Kingston has four times the number of mathematicians that Onteora has. There are exactly two areas that have two mathematicians. Neither Rhinebeck nor Red Hook have only one mathematician. From this information, can you find out how many mathematicians are coming from each area?One last math moment to share!I noticed that if I represent the number of eighth graders as “n”, the number of seventh graders is 2n-1, the number of boys is 2n+1, and the number of girls is n-2. Given that we have 23 incoming mathematicians that are either in seventh or eighth grade, and are either a boy or a girl, can you figure out how many mathematicians are in seventh grade? Eighth grade? Are boys? Are girls?This is only a taste of what’s to come! As we get ready to welcome new mathematicians to Bard, we are sure to stumble upon some more problems hiding under the floorboards, behind whiteboards, and all sorts of unexpected places. Hope to see you soon!-Justin Shin