#### Sisi is a very compassionate person, and that's reflected in the time she devotes to leading the school's Beta Club, a volunteer group of honors students. The club is currently raising money for victims of the recent tsunami in southeast Asia. But Sisi, who was born in China and came to the U.S. in 1989, feels little compassion for numbers — certainly not 1s.

She set out to find an equation for expressing any given number with the fewest 1s, using only addition and multiplication. That's a classic math problem, and each generation of mathematicians strives for a more elegant solution. Sisi's contribution was to see if including subtraction in the arithmetic equation could further reduce the 1s needed. She suspected it would. "Surprisingly," she says, "I proved there are infinitely many integers [where] allowing subtraction does not reduce the number of 1s necessary to express a number."

On the other hand, "I also proved there's an infinite number of different possible cases where subtraction does help." Confused? Sisi chuckles and says some of her math friends were, too, for a bit. It can take a moment to realize that one proof doesn't exclude the other — just as "an infinite number of integer strings ending in an odd digit" doesn't rule out strings ending with an even digit. Finally, Sisi's paper established upper and lower bounds for solving least-1s problems with or without subtraction.

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