A will specifies that several diamonds, to be found in a safety deposit box, are to be distributed to the deceased's children as follows: half of them to the eldest, one quarter of them to the middle child, and one fifth to the youngest. The executor is puzzled about what to do when it turns out that there are nineteen identically sized diamonds in the box. You can't give out half, one quarter, or one fifth of this collection without cutting some diamonds into pieces, and cutting a diamond would ruin its value. What can the executor do?
The executor hits on this ingenious plan: he borrows another diamonod of the same size from a jeweller friend, and adds it to the nineteen. He takes half of the twenty-ten of them- and gives them to the eldest child; then one quarter of the twentry-five-to the middle child; and one fifth of the twenty- four-to the youngest. He has distributed nineteen diamonds; one remains-the one he borrowed from the jeweller-which he now returns. The eldest child is delighted, reasoning that she was entitled to only nine and a half diamonds (one half of the nineteen) but has received ten instead; the ther two think they have received a similar bonus.
A QUESTION TO THINK ABOUT: Something is peculiar about this very nifty solution. Do you see what has gone wrong? (Hint: there's something wrong in the terms of the will.)