Cups
Written on 2:46 pm by Vja Students
Chaitu,Balaji & Dileep sit at a round table. On the table, there are 12 cups full of tea. Every day, at 6 o'clock, each of the table-companions move two places to his right or left (if the place is free) and drinks all the tea at that place, if there is any in his cup. After the place changing, Karthik fills one of the cups. In this way, at least how many cups can Karthik keeps full ?
Ans: Karthik can always keep at least 7 cups filled. He only has to seat the three dinners alternating. Thus 6 cups will be always untouched. And he can always fill 1.
If we mark that there are 12 chairs 1-12 around the table and at every place one cup of tea available.Now there may be followin cases -
1. If all the campaninons occupying even place like 2nd, 4th, 6th.... on the table then they can move 2 places left or right. In that case they can grab tea of only even place and odd place will reamain untouched ..then Kartik will fill 1......
7 will be filled - 6 odd + 1 by Kartik.
2. Same with the case if people occupying all the odd places the all even places will be untouched then again 7 (6 even + 1 Kartik)
3.If they are occupying any even and odd both then in the last only 1 cup of tea will be filled there ..which is by Kartik every day.
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(Actually, I couldn't understand the question very properly, but here is my try.)
Chaitu,Balaji & Dileep sit at the round table two places apart. So, everyday, only Dileep (or Chaitu) gets tea everyday, while the other two get tea for only the first day after which they have to sit on places with empty tea cups left by their earlier friend. Kartik just has to fill the last tea cup of Chaitu (or Dileep) Thus, everyday two cups of tea will be empty. Hence, he can keep ten cups full everyday if he uses this arrangement. Minimum is reduced from 10 on the first day to just one after a few days if we use other placements.