1994 AMC 12 Problem 19
Attempt Problem 19 of the 1994 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1994 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Label one disk “,” two disks “,” three disks “,” fifty disks “.” Put these labeled disks in a box. Disks are then drawn from the box at random without replacement. The minimum number of disks that must be drawn to guarantee drawing at least ten disks with the same label is
Answer: C
Small hint:
Count the most disks that can be drawn while taking at most nine of each label
Big hint:
All disks labeled through may be drawn, but only nine of each label through
Solution:
To avoid ten equal labels, one may draw all disks with labels below and at most from each of the labels through Thus disks can be drawn without forcing ten alike, and the next draw guarantees them. The minimum is Thus the correct answer is C.
Problem 19 in other years
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