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 diamonds.
Mary would get 1/20 of the diamonds or 2 and 19/20 diamonds.
Johnny would get 1/60 of the diamonds or 59/60 diamonds.

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 diamonds.
Mary would get 1/20 of the 60 diamonds or 3 diamonds.
Johnny would get 1/60 of the 60 diamonds or 1 diamond.

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 further comment.

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?