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Blocked Off

Jeff had fewer than 100 blocks. When he made five equal rows, he had one left over; with four equal rows, he had one left over; and with nine equal rows, he had none left over. How many blocks did Jeff have?


Suppose that all the conditions about Jeff's blocks remain except that he has fewer than 1000 blocks. How many blocks might Jeff have?

(Source: Adapted from Mathematics Teaching in the Middle School, Jan-Feb 1995).

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