Find Integer Solutions for Tricky Equations with Maximum Error of +- pi/7

[PseudoComplex]

Given 3 equations:

1) 1/2pi + 2Pi(x) = 3.90625F
2) pi + 2Pi(y) = 7.65625F
3) 3/2pi + 2Pi(z) = 11.2500F

Find such F so that x, y and z are integers; maximum error on the left side can be +- pi/7.

How would you tackle this one? I am still trial'n'erroring..

 

[HallsofIvy]

?? Those are basically just arithmetic problems aren't they? First pi/7 is approximately 0.44880 so that's the accuracy you need- not very accurate at all! Using five decimal place accuracy to start with should be enough. Assuming that by "1/2pi" you mean (1/2)pi and not 1/(2pi), then the first equation becomes 1.57080+ 6.28318x= 3.90625F. Solve for x:
6.28318x= 3.90625F- 1.57080. Divide by 6.28318: x= .62170F- .25000. Do the same for y and z. It should not be hard to find a value for F so that each of those will be within pi/7 of an integer.