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8 in a Row

Age 11 to 14 Short Challenge Level:

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these integers?

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8 Methods for Three by One

Age 14 to 18 Challenge Level:

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different?. . . .