Black Purse and White Purse
James has many 1-dollar, 2-dollar, and 5-dollar coins. He put 6 coins in his white purse and 8 coins in his black purse such that the amount of money in the black purse is same as that of white purse and if we RANDOMLY get two coins from each purse and put them into the other purse, then the difference between the amount of money in the two purse MUST be 4 dollars. Find the total amount of money in the two purse.
The answer is 24.
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1 solution
If the white purse contains 2 , 2 , 2 , 2 , 2 , 2 and the black purse contains 1 , 1 , 1 , 1 , 1 , 1 , 1 , 5 , then both purses contain 1 2 dollars. Two coins from the white purse will always total $ 4 . Two coins from the black purse will total either $ 2 or $ 6 . Thus, then two coins from the two purses are swapped, the difference in the purse totals will always be $ 4 . This makes the answer 1 2 + 1 2 = 2 4 .