There was an old gentleman who
lived in Alderson who shall remain nameless. He
spent his working life in Africa mining
diamonds. He, unknown to local folks, was quite
rich in diamonds that he kept under the floor
boards in his modest home. Upon his death, it
was found that his will specified the location
of 59 quite large diamonds that were to be
distributed among his heirs according to the
specifications given in his will. The
instructions in the will were as follows:
Bob is to get 1/2 of the diamonds.
Janet is to get 1/4 of the diamonds.
Frank is to get 1/6 of the diamonds.
Mary is to get 1/20 of the diamonds.
Johnny is to get 1/60 of the diamonds.
The will also pointed out that the diamonds
could not be cut in any manner.
The heirs and the lawyer who was administrator
of the will gathered in the lawyer’s office,
where the diamonds were laid on a table, and
they made the following calculations:
Bob would get 1/2 of the 59 diamonds which
turned out to be 29 and 1/2 diamonds.
Janet would get 1/4 of the diamonds which would
be 14 and 3/4 diamonds.
Frank would get 1/6 of the diamonds or 9 and 1/6
Mary would get 1/20 of the diamonds or 2 and
Johnny would get 1/60 of the diamonds or 59/60
But the will specified that the diamonds could
not be cut in any manner. Upon seeing how this
worked out, the heirs cursed the old man saying
that he had played a dastardly trick on them and
they would not get an inheritance after all.
About that time Boozer, a wise and long time
resident of Alderson showed up in the lawyer’s
office. Why he was there was not pointed out,
but he was there none-the-less. Boozer looked
over the problem and smiling said “I think I can
solve your problem. I just happen to have a
small diamond in my pocket” and he placed his
diamond on the table with the other 59 larger
diamonds. Boozer instructed the group to make
their calculations again, but this time with 60
diamonds. But the group of heirs questioned his
method, since they felt that Boozer would lose
his diamond and that they would be beholden to
him. They felt that Boozer might try to extract
money from them in the future for solving their
problem. But Boozer just smiled and said “Just
do as I say and everything will work out.” So
the calculations were made again.
Bob would get 1/2 of the 60 diamonds which
turned out to be 30 diamonds.
Janet would get 1/4 of the 60 diamonds which
would be 15 diamonds.
Frank would get 1/6 of the 60 diamonds or 10
Mary would get 1/20 of the 60 diamonds or 3
Johnny would get 1/60 of the 60 diamonds or 1
At this point each heir took his or her share of
the diamonds. After this was done it was noticed
that Boozer’s small diamond was still on the
table. So did one the heirs make a mistake and
pick up one less of the diamonds that he or she
was to receive? Well, let’s see. If we add up
the diamonds that each heir was to receive, the
sum should be 60 shouldn’t it? Well, 30 + 15 +
10 + 3 + 1 = 59
The heirs and the lawyer didn’t know what to
say. At this point Boozer pocketed his diamond
and said “fooled you didn’t I. You thought I was
going to lose my diamond, but I knew better.”
Boozer smiled at the group and then he turned
and walked out of the lawyer’s office without
Postscript: Is this a flaw in mathematics? Does
this point out that mathematics is not safe to
use to build airplanes, cars, trains, etc.? Or
is there a flaw in how Boozer set up and solved
the heir’s inheritance problem?