$[$#$361$a$]$ How much room does a juggler need? $($part $1)$

A juggler throws balls almost vertically upwards, with time $t=0\mathrm{.}23s$ between each throw. $($Yes$,$ pretty amazing.$)$ The balls are all thrown to the same height, and in repeated succession $($e$.$g$.1,2,3,1,2,3$ etc.$).$ Let's simplify: neglect air resistance, neglect the time between catching and throwing a ball and assume that balls are thrown and caught at the same height. Calculate the minimum height he must throw the balls if he is to juggle

$3$ balls?

$($Hints: How many throws before the same ball gets thrown again? How does the time for the ball to go up compare with the time to go down?$)$