A shoemaker died, leaving behind 17 pairs of men's shoes and boots. In his last will and testament he disposed of them as follows: 1/2 of the collection to his youngest, hardworking, son; 1/3 to the middle son; and 1/9 to "Lazybones", the eldest son.

Understanding that it was not possible to divide the 17 pairs into halves, thirds, and ninths, the exasperated executor of the will tossed in his own footwear, making it a total of eighteen pairs, which he divided as follows: 1/2, or 9 pairs, to the youngest son; 1/3, or 6 pairs, to the middle son; and 1/9, or 2 pairs, to the eldest son.

Upon realizing that adding up 9, 6, and 2 made 17, the executor elatedly retrieved his own pair of shoes and closed the estate.

Question: What's the mistake in the shoemaker's
problem?