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Sahana Vasudevan, 16, of Palo Alto, entered an Intel Science Talent Search project in mathematics that proves a new, generalized way to minimize carries. Carries are important in arithmetic; for example 7 + 6 = 3 with a carry of 1. In computing, the carry is usually handled by a "carry bit," so reducing carries decreases computational load. With the usual choice of digits, one is forced to carry about half the time, but previous work had shown that in odd prime bases, digits could be chosen so that the probability of a carry is reduced to 25 percent and that no further reduction is possible. Sahana generalized this result to mathematical structures called "groups" and proved that, in this general case, the set of digits must satisfy a certain necessary condition for the probability of a carry to be less than 25 percent. Sahana is fluent in Tamil, her first language, and is an award-winning Carnatic (South Indian Classical) vocalist and violinist, having honed her singing talents since she was four and played violin since age seven. Last summer, she performed on a Carnatic music concert tour in India. Sahana is a student at Gnyanam Academy (Homeschool) and is the daughter of Jayaraman Vasudevan and Vanaja Narayanaswamy.
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