Find the number of solutions of the equation:

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[x]+[2x]+[4x]+[8x]+[16x]+[32x]=12345

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where [.] denotes the greatest integer function.

let {x}=x-[x},there is one solution each for 0≤{x}<(1/32),(1/32)≤{x}<(1/16),(1/16)≤{x}<(1/8),(1/8)≤{x}<(1/4),(1/4)≤{x}<(1/2)and(1/2)≤{x}<1, therefore there are a total of six solutions