Map created from Claude Shannon's juggling theorem for the juggling pattern known as the Shower, synchronous (4x,2x). (F+D)H = (V+D)N.
F = time in air
D = time in hand
H = number of hands
V = time hand is vacant
N = number of ballsThus for the three ball Shower: (2+1)2 = (1+1)3 = 6.

A three ball pattern for one person, we know that, H = 2 and N = 3, thus:
(F+D)2 = (V+D)3.
The LCD of 2 and 3 is 6. The only option for x*2 = y*3 is that x is three and y is two.
This means that V and D must equal 1 each, so that their sum equals two:
(F+1)2 = (1+1)3.
Since D = 1, the only option for F is 2, so that their sum is three, thus:
(2+1)2 = (1+1)3 = (3)2 = 2(3) = 6.
Own work
Hyacinth