Matt is the fiftieth fastest and the fiftieth slowest runner in his school. Assuming no two runners are the same speed, how many runners are in Matt’s school?
Answer: There are 99 runners in Matt’s school.
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Picture three boxes containing fruit. The first box is marked peaches, the second is marked oranges, and the third box is marked peaches and oranges. Each of the boxes is labeled incorrectly. How could you label each box correctly if you were allowed to select only one fruit from one of the boxes?
Answer: First you select a fruit from the box marked peaches and oranges. If it was a orange you selected, you know that the box could only contain oranges. If it was a peach, you know that the box could only contain peaches since each box is incorrectly marked. If, for example an orange was selected, you would mark that box oranges and switch the other two incorrect labels around. Now all three would be correctly labeled.
Solution:
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First you select a fruit from the box marked peaches and oranges. If it was a orange you selected, you know that the box could only contain oranges. If it was a peach, you know that the box could only contain peaches since each box is incorrectly marked. If, for example an orange was selected, you would mark that box oranges and switch the other two incorrect labels around. Now all three would be correctly labeled.
Show Answer
First you select a fruit from the box marked peaches and oranges. If it was a orange you selected, you know that the box could only contain oranges. If it was a peach, you know that the box could only contain peaches since each box is incorrectly marked. If, for example an orange was selected, you would mark that box oranges and switch the other two incorrect labels around. Now all three would be correctly labeled.
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