The point is to "numerically" estimate the ten numbers whose sum is greatest given that the sum of their squares is less than one.
q(a,b,c,d,e,f,g,h,i,j) = a+b+c+d+e+f+g+h+i+j
maximum(q(a,b,c,d,e,f,g,h,i,j) for a in 0:0.0001:1, b in 0:0.0001:1, c in 0:0.0001:1, d in 0:0.0001:1, e in 0:0.0001:1, f in 0:0.0001:1, g in 0:0.0001:1, h in 0:0.0001:1, i in 0:0.0001:1, j in 0:0.0001:1 if a^2+b^2+c^2+d^2+e^2+f^2+g^2+h^2+i^2+j^2 < 1)
My solution is of a brute force form which seemed fine for a smaller problem - the sum of only two such numbers - but is painful for larger n.
q(a,b) = a+b
maximum([q(a,b) for a in 0:0.0001:1,b in 0:0.0001:1 if a^2 + b^2 < 1])