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Three people have 32,32,72, and $98, respectively. If they pool their money then re-distribute it among themselves, what is the maximum possible value for the median amount of money?

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Assuming the values are 32, 72 and 98 and distributing in fractions or not distributing at all is not allowed.

Total sum = 202.

For median, there should be a value which is lower than that value, and a value which is higher than that. Since we want to get high median we can keep the lowest value = 1. Now, $201 is left. We have to divide it in 2 people such that the lower amount(which will be the median) can be maximized. This can be done when the 2 values are as close as possible i.e 100 and 101. Thus answer = 100.

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