The Great Scramble
Answer :

The smallest number of sugar plums that will fulfil 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.

Math Genius