Problem:
Two children at a time can play pairball. For minutes, with only two children playing at one time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is
Answer Choices:
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Solution:
Two children are playing at the same time, so there are minutes of playing time. This must be divided equally ways, so each child gets minutes.
If pairball were played by one person at a time, each child would get of , or minutes of playing time. Since two players are required, each child gets double this, or minutes.
There are ways to pair the children, so each session lasts minutes. Each child is paired with four other children, so each child will play for minutes.
Query. What are the ways to pair the five children?
At any given time, children are playing and are not, so of the children are playing at any given time. This implies that each child plays of the time. Thus, each child plays minutes.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions