(related to Problem: The Great Scramble)
The smallest number of sugar plums that will fulfill the conditions is $26,880.$ The five boys obtained respectively: Andrew, $2,863;$ Bob, $6,335;$ Charlie, $2,438;$ David, $10,294;$ Edgar, $4,950.$ There is a little trap concealed in the words near the end, "one-fifth of the same," that seems at first sight to upset the whole account of the affair. But a little thought will show that the words could only mean "one-fifth of five-eighths", the fraction last mentioned — that is, one-eighth of the three-quarters that Bob and Andrew had last acquired.
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