Arabic Problem

This is an old arabic problem:

An old man had 11 horses. When he died, his will stated the following distribution to his 3 sons:
1/2 gives to the eldest son,
1/4 for 2nd son,
1/6 for 3rd son.

Find: how many horses each son gets ?

There are 2 methods to solve: first using simple arithmetic trick without knowing the theory behind; the second method will explain the first method “from an advanced standpoint” – Number Theory (Felix Klein’s Vision )

1) Arithmetic trick:

11 is odd, not divisible by 2, 4 and 6.

Loan 1 horse to the old man:
11+1 = 12

1st son gets: 12/2 = 6 horses
2nd son gets:12/4 = 3 horses
3rd son gets: 12/6 = 2 horses

Total = 6+3+2=11 horses

Up to you if you want the old man to return the 1 loan horse 🙂

Strange! WHY ?

2)