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Puzzle 31.  CRYPTARITHM

Sally needs money and send the following puzzle to his father who is a mathematics professor:

 N E E D + M O R E
 _______________________________
 C A S H

She asks him to send her the dollar amount represented represented by the word CASH in the above puzzle.  She has a solution:

6449+1754=8203.

Therefore, she expects to receive \$8203.  However, her mathematically minded father knew that there are numerous solutions to this cryptarithm.  So he sent her the minimum dollar amount represented by the word CASH.  How much did he sent her, and what was his solution to this cryptarithm?

Sally's solution is also not the maximum amount that can be represented by the word CASH.  Can you solve what is the maximum amount allowed by the puzzle?

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Bits and Beyond ...

PERFECT NUMBERS

An integer is called a perfect number if it is equal to the sum of all of its positive factors, excluding itself.  The first perfect number is 6 because 6=1+2+3, where 1, 2 and 3 are the factors of 6.  The next is 28 because 28=1+2+4+7+14.  The next two are 496 and 8128.

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