# dividing the cows [duplicate]

This is a well-known local puzzle.

An old farmer has 17 cows and three sons. After his death, this is what the will contains: "I have decided that the livestock will be distributed among the three sons like so: A, the oldest, will get half of all cows. B, the middle son, will get a third of all. C, the youngest, will get a ninth.

No cow is to be harmed, or partly owned; otherwise no one gets any, and the cows are to be given away to the village."

How do the sons resolve this puzzle?

## marked as duplicate by xnor, f'', Zerris, Lawrence, AlexisJan 1 '16 at 14:04

• Why the downvote? Please explain. – cst1992 Jan 1 '16 at 6:50
• It could be, there are many variants. They must use camels in Rajasthan, and cows in Maharashtra. – cst1992 Jan 1 '16 at 9:23

Let's take a token cow and assume it to be a part of the old man's inheritance.

Now there are 18 cows.
1/2 of 18 = 9. The 1st son gets 9.
1/3 of 18 = 6. The 2nd son gets 6.
1/9 of 18 = 2. The 3rd son gets 2.

There is no condition on the no. of cows that remain after the distribution has been done.
9+6+2 = 17.

Everyone gets what's in the will. The token cow is the extra one.

• That's pretty much the exact answer. Only difference is that the token cow is of a relative. – cst1992 Jan 1 '16 at 6:34
• @Ahmed Ashour .. What was the need to fix a 2 years old question just for the sake of putting the spoiler tag ? – Maniraj Jun 6 '18 at 12:24
• @Maniraj: spoilers are recommended, regardless of being old or not. Also, getting 2 points by editing them. – Ahmed Ashour Jun 6 '18 at 12:28
• @AhmedAshour If its like that we can ask the moderators to do something regarding that as there are loads of questions where the spoiler tag is missing. Editing these old questions gives them unnecessary attention and the new questions goes down in the list and hence they don't get the required attention. – Maniraj Jun 6 '18 at 12:32

These three brothers asked me to help them to distribute cows.

I just added a cow owned by me. So the total number of cows are 18.

The cows are distributed as below.
For A:

18/2 = 9 cows (half of all cows)

For B:

18/3 = 6 cows (third of all cows)

For C:

18/9 = 2 cows (ninth of all cows)

Total

9+6+2 = 17 ... So I will take my cow back.