Two Functions Having Something Common

Algebra Level 4

Given that f(x)=sinxf(x)=\sin x and g(x)=x/10g(x)=x/10. If x1,x2,...,xnx_{1},x_{2},...,x_{n} are the values of xx for which f(x)=g(x)f(x)=g(x), then find the maximum possible value of x1x2+x3x4+±xn1n1.\dfrac {\left\lfloor x_{1}\right\rfloor- \left\lfloor x_{2}\right\rfloor+\left\lfloor x_{3}\right\rfloor-\left\lfloor x_{4}\right\rfloor+\cdots\pm \left\lfloor x_{n}\right\rfloor-1}{n-1}.

Details and Assumptions

  • \left\lfloor\cdot\right\rfloor represents the Floor Function.
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