SOLUTION: Bob has 50 pennies and 6 cups. He put even number of pennies in each cup. What is the least number of pennies the cup with the most pennies can have?
Question 1126665: Bob has 50 pennies and 6 cups. He put even number of pennies in each cup. What is the least number of pennies the cup with the most pennies can have? Found 2 solutions by ikleyn, jim_thompson5910:Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website! .
The least number of pennies the cup with the most pennies can have, is achieved when 8 pennies are in each of 5 cups
and 10 pennies are in the 6-th, the last cup.
This number under the question is then 10.
Divide the total amount of pennies over the number of cups to find the quotient and remainder
50/6 = (48+2)/6 = 48/6 + 2/6 = 8 remainder 2
This tells us that we can place 8 pennies into each of the six cups, and have 2 left over. Let's place those two leftover pennies into the last cup. We do this to ensure that this cup has the most amount of pennies. If we split the two pennies up among 2 cups, then we'd have two cups tied for first place in terms of having the most pennies. Also, we need to ensure that each cup has an even number of pennies. This isn't possible if we go from 8 to 9 pennies. So again we deposit the two pennies together into the sixth cup. Therefore, the smallest amount of pennies in the sixth cup is 8+2 = 10 pennies.
Answer: 10
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Side Note:
The smallest amount of pennies in one cup is 2 assuming each cup must be filled in some way. If we do this for five cups, then we have 5*2 = 10 pennies taken care of so far. That means we have 60-10 = 50 left over. This is the largest amount of pennies we can place into the sixth cup. The range of pennies for the sixth cup spans from 10 to 50 inclusive of both endpoints.
If there is no restriction on whether a cup is empty or not, then the most pennies we can place into a single cup is of course 50 pennies; however, that seems a bit too trivial which is why I think the restriction is in place.