There are 18 boxes, so the average number of boxes to guarantee a full key are 9 boxes or 10 boxes (actually 9.5) . This means 95 stars daily needed on average, to unlock the key.
But with 50 stars given daily, there is only
(50 / 95 ) ^ 32 , chance to complete the calendar just by luck , since
(50 / 95 ) ^ 32 = 0.526 ^ 32 = 1.2 x 10 ^ (-9), which is barely just over 1 in a BILLION odds.
of course, to improve odds, you can win some key parts in challenges (1 up to 4) , but as you see , 5 key parts are needed for 1 full key, so the chances are never fair.
Therefore I would argue that it's almost impossible to finish the calendar without spending diamonds.
(unless you fancy ' 1 in a billion' or '1 in a million odds')