THE GREAT SCRAMBLE.
(
Money Puzzles)
After dinner, the five boys of a household happened to find a parcel of
sugar-plums. It was quite unexpected loot, and an exciting scramble
ensued, the full details of which I will recount with accuracy, as it
forms an interesting puzzle.
You see, Andrew managed to get possession of just two-thirds of the
parcel of sugar-plums. Bob at once grabbed three-eighths of these, and
Charlie managed to seize three-tenths also. Then young David dashed upon
the scene, and captured all that Andrew had left, except one-seventh,
which Edgar artfully secured for himself by a cunning trick. Now the fun
began in real earnest, for Andrew and Charlie jointly set upon Bob, who
stumbled against the fender and dropped half of all that he had, which
were equally picked up by David and Edgar, who had crawled under a table
and were waiting. Next, Bob sprang on Charlie from a chair, and upset
all the latter's collection on to the floor. Of this prize Andrew got
just a quarter, Bob gathered up one-third, David got two-sevenths, while
Charlie and Edgar divided equally what was left of that stock.
They were just thinking the fray was over when David suddenly struck out
in two directions at once, upsetting three-quarters of what Bob and
Andrew had last acquired. The two latter, with the greatest difficulty,
recovered five-eighths of it in equal shares, but the three others each
carried off one-fifth of the same. Every sugar-plum was now accounted
for, and they called a truce, and divided equally amongst them the
remainder of the parcel. What is the smallest number of sugar-plums
there could have been at the start, and what proportion did each boy
obtain?
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.
