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**juan.manuel.prada29****Member**- Registered: 2016-06-28
- Posts: 4

We have an urn with 496 marbles of 4 different colors (we don't know the distribution of the colors). If we randomly pick 397 marbles, it is guaranteed that we pick at least one from each color. What is the minimum number of marbles we need to pick, in order to be able to guarantee that we will have 3 colors?

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,051

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**juan.manuel.prada29****Member**- Registered: 2016-06-28
- Posts: 4

I believe it is correct - solution please? All I managed to do is that the 4th color has 496-396=100 marbles (so in order to have 4 colors, we must pick 496-100+1=397.

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,051

The 4th color is the one having least marbles =100. All others have > or = 100 marbles. so the 3rd largest color must have at least 100 marbles. so 396-100 will leave at the least 2 colors. adding 1 to make it 297 assures 3 colors.

*Last edited by thickhead (2016-06-29 04:36:04)*

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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