Same 10 Coins Needed
One coin is labeled with the number 1, two different coins are labeled with the number 2, three different coins are labeled with the number 3, ............,forty-nine different coins are labeled with the number 49, and fifty different coins are labeled with the number 50. All of these coins are then put into a black bag. The coins are then randomly drawn one by one. We need 10 coins of any same type. What is the minimum number of coins that must be drawn to make sure that we have at least 10 coins of one type?
The answer is 415.
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1 solution
In the worst case scenario, we have to draw 9 coins (or all, if there is less than 9 altogether of a type (1 to 8), e.g. all 7 coins with the number 7 on them) and a last coin, which then will be the 10th of its kind.
Therefore, our answer should be:
( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 ) + 4 2 × 9 + 1 = 4 1 5