Pensieve header: January 20: The 1206 Riddle.

Tuples[{1,-1},3]

?Ball

Graphics3D[Ball /@ Tuples[{1,-1},3]]

Graphics3D[{Yellow,Ball /@ Tuples[{1,-1},3],Blue, Ball[{0,0,0},(Sqrt[3])-1]}]

((2 (π^(n/2)) (r^n))/(n (Gamma[(n/2)])))

r[n_]:= N[(((2 (π^(n/2)) ((((Sqrt[n])-1))^n))/(n Gamma[(n/2)]))/(4^n))]

r[2]

r[3]

Table[r[n], {n,2,10}]

Table[r[n], {n,2,100}]

r[1000000]

r[1000]

ListPlot[Table[r[n]//Log,{n,2,2000}]]

n=2;While[r[n]<1,++n];n