Question 1106130: A lady has 55 earrings in her jewel box: 21 pair of platinum earrings, 15 pair of gold earrings and 17 pair of silver earrings. The lights went out and she is completely in the dark. How many earrings must she take out to make 100% certain she has a pair of gold earrings?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! If she takes out 15 pairs, then she could still have
all silver, all platinum, or a mixture of those
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The same is true if she took out 17 pairs
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If she took out 21 pairs, she could have all platinum,
or a mixture of platinum and silver
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If she took out 21 + 17 = 38 pairs, she could have
all platinum and all silver
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If she took out 39 pairs, she is 100% certain to have
at least 1 pair of gold
Answer by ikleyn(52858)  (Show Source):
You can put this solution on YOUR website! .
A lady has 55 earrings in her jewel box: 21 pair of platinum earrings, 15 pair of gold earrings and 17 pair of silver earrings.
The lights went out and she is completely in the dark. How many earrings must she take out to make 100% certain she has a pair of gold earrings?
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1. Everything is OK with your problem, except one thing:
The number 55 is not equal to the sum of 21, 15 and 17, as one could expect . . .
2. The standard, usual and traditional form/way of presenting the solution to this / (to such) problem/problems are THESE three lines:
In the worst case, in the dark, she will take out 21 pair of platinum earrings and 17 pair of silver earrings first,
i.e. 21 + 17 = 38 items, in all.
But as soon as she takes out the 39-th item, she will have the gold earrings inevitably, making 100% certain.
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