Label one disc as “1”, two discs as “2”, three discs as “3”,…., sixty three discs as “63”.
These 1+2+3+...+63 = 2016 labeled discs are put in a box.
Discs are then drawn from the box at random without replacement.
(i) What is the minimum number of discs that must be drawn in order to guarantee drawing at least ten discs with the same label?
(ii) Will the answer change if discs were drawn from the box with replacement?
(In reply to re: Solution
by Ady TZIDON)
Part (ii) in more detail:
Some number will eventually be drawn ten times.
In the worst case scenario, each of the (63) labels could be drawn nine times before this happens. (9*63)
If this happens, the next draw is then guaranteed to be the tenth draw of some label. (9*63 + 1).
[The reason this is slightly higher than part (i) is that the labels 1 through 8 cannot be drawn nine times.]
Posted by Jer
on 2016-08-25 14:06:33