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Labeling Minimum (Posted on 2016-08-25) Difficulty: 2 of 5
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?

No Solution Yet Submitted by K Sengupta    
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Solution Solution | Comment 1 of 4
(i) First find the maximum number that can be drawn without having 10 of any.
1+2+...+8+9+9+9+...+9=531
The add one.  The 532nd draw is guaranteed to create a set of 10.

(ii) The answer to the question as written is a simple Yes
Finding the actual number is similar except now the small numbers of "1", "2" don't matter.
63*9=567
Answer 568

  Posted by Jer on 2016-08-25 10:19:08
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