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At the classroom costume party the average age of the (b) boys is g and the average age of the (g) girls is b. If the average age of everyone, including the 42-year-old teacher, is b+g, what is the value of b+g?

take a number, greater than 1. if odd, subtract 1, square it. if even, divide by 2. 2 -> 1 3 -> 4 -> 2 5 -> 8 -> 4 7 -> 36 --> 9 -> 16 -> 8 11 -> 100 -> 25 -> 576 -----> 9 13 -> 144 ----> 9 will this always hit a power of 2?

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hello, i was wondering if any of you can help me figure this out. I'm playing a game of rock-paper-scissors against a computer. My goal is to win 15 times in a row. Let's say that the computer picks rock/paper/scissors in a completely random way; it doesn't use a pattern nor does it have AI. My question is, if I were to play against the computer non-stop until i meet my goal (or i die), which approach would have the best chance of getting 15 wins in a row? A. Keep playing ROCK all the way. B. Using a pattern i.e. ROCK -> PAPER -> ROCK -> SCISSORS -> PAPER -> SCISSORS then repeat C. Randomly choosing between rock/paper/scissors every round. D. They are all equally bad/good. E. The above are all crap, use this --> (INSERT BEST APPROACH HERE). F. Other answer. (please specify)

There are two fractions, 34/55 and 55/89. We are looking for a third fraction of positive integers a/b, where 34/55>a/b>55/89 and 55<b<89. What is the smallest b where this is possible?