Lamps, Factorizations, and Finite Fields
نویسنده
چکیده
The origin of this study is the 1993 International Mathematical Olympiads, held at Istanbul, Turkey. Problem # 6, which occurred on day 2, reads: Let n > 1 be an integer. There are n lamps L0, . . . , Ln−1 arranged in a circle. Each lamp is either ON or OFF. A sequence of steps S0, S1, . . . , Sj , . . . is carried out. Step Sj affects the state of Lj only (leaving the state of all others lamps unalterated) as follows: if Lj−1 is ON, Sj changes the state of Lj from ON to OFF or from OFF to ON; if Lj−1 is OFF, Sj leaves the state of Lj unchanged. The lamps are labeled mod n, that is,
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 107 شماره
صفحات -
تاریخ انتشار 2000