# HG changeset patch # User Shlomi Fish # Date 1378908782 -10800 # Node ID dc5b4ae9bcc0d81c88a0a085509c0b63e3bc6eba # Parent 4411cf55c38d1acb3662200ba797b521695df53a Add more to the analysis diff --git a/project-euler/137/analysis.txt b/project-euler/137/analysis.txt --- a/project-euler/137/analysis.txt +++ b/project-euler/137/analysis.txt @@ -11,3 +11,32 @@ x/(2*\$s) * { (1+\$s)/[1 - x(1+\$s)/2] - (1-\$s)/[1 - x(1-\$s)/2] } = x/(2*\$s) * { 1/[1/(1+\$s) - x/2] - 1/[1/(1-\$s) - x/2] } = + + [y = x/2] + +y*\$s * {1/[1/(1+\$s) - y] - 1/[1/(1-\$s) - y] } = + + [z = 1/y] + +\$s * { 1 / [z/(1+\$s) - 1] - 1 / [z/(1-\$s) - 1] } = N + +\$s * [z/(1-\$s)-1 - z/(1+\$s) + 1 ]/[z/(1+s)-1]/[z/(1-s)-1] = N + +\$s * z * (1/(1-\$s)-1/(1+\$s)) = N[z/(1+\$s)-1][z/(1-s)-1] + + [ * (1+\$s) * (1-\$s)] + +\$s * \$z * (1+\$s-1+\$s) = N[z-(1+\$s)][z-(1-\$s)] + + 2 \$s^2 * \$z = N [ z^2 - 2z + (1-\$s^2)] + + \$s^2 = 5 + + 10z = N [ z^2 - 2z - 4 ] + + z^2 - (2+10/N)z -4 = 0 + + z = [ -2a +/- sqrt(b^2-4ac) ] / (2*a) + + +