Ghost in the machine
Presh Talwalkar's Mind Your Decisions channel has only recently come to my random YouTube recommendations, so puzzles that prove that mathematicians believe in ghosts is now five years old. But puzzle 1 is annoying, because its solution is fundamentally wrong.
A father leaves seventeen goats to his three sons. His will specifies that one half of the goats go to the oldest son, one third to the middle son, and one ninth to the youngest son. But there is a problem. Seventeen cannot be split evenly to any of these fractions. So how did the sons divide up the goats fairly according to their father's wishes?
The trick to answering this puzzle is to add an eighteenth imaginary, ghost
, goat. The goats can now be divided among the sons, with nine (one half) going to the oldest son, six (one third) going to the middle son, and two (one ninth) going to the youngest son. The imaginary goat can disappear and, according to Presh, the sons have divided the goats according to the father's wishes
.
Except they haven't, Presh. They actually have nine seventeenths, six seventeenths, and two seventeenths respectively; all of which are about 6% higher than their father's wishes.
The correct answer is that the father was quite clearly not the full ticket on his deathbed. And the puzzle doesn't show that mathematicians believe in ghosts, it shows that they have no grip on reality. (oldman)