Neighbour’s Cows

An old farmer died and left 17 cows to his three sons. In his will, the farmer stated that his oldest son should get ¹/₂, his middle son should get ¹/₃, and his youngest son should get ¹/₉ of all the cows. The sons, who did not want to end up with half cows, sat for days trying to figure out how many cows each of them should get. One day, their neighbour came by to see how they were doing after their father’s death. The three sons told him their problem. After thinking for a while, the neighbour said: “I’ll be right back!” He went away, and when he came back, the three sons could divide the cows according to their father’s will, and in such a way that each of them got a whole number of cows.

What was the neighbour’s solution?

The neighbour borrowed an extra cow, to make the total number of cows 18. Then the oldest son got ¹/₂ of 18 is 9 cows, the middle son got ¹/₃ of 18 is 6 cows, and the youngest son got ¹/₉ of 18 is 2 cows. Since 9+6+2 = 17, the cows could be divided among the three brothers in such a way that the borrowed cow was left over, and could be returned to its owner.