### Brain Teasers

# Share the Money

Nine boys and three girls agreed to share equally their pocket money. Every boy gave an equal sum to every girl, and every girl gave another equal sum to every boy. Every child then possessed exactly the same amount. What was the smallest possible amount that each child then possessed?

### Answer

Every boy and girl had three cents at the beginning. Then every boy gave one cent to every girl and the boys were left with nothing and the girls were left with 12 cents each. Then every girl gave one cent to every boy and they were all finally left with three cents each.Hide Answer Show Answer

## What Next?

View a Similar Brain Teaser...

If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.

### Solve a Puzzle

## Comments

Nov 06, 2001

this answer is not correct. the same calculation could be made giving each child 9 cents less. they could still swap the same amounts and would only have 9 cents each at the end

Actually, if the boys start with the minimum 3 cents and the girls with 15, the boys can give 1 cent, and the girls can give 2 and they will all have 6 cents.

also if everyone starts off with 0 and gives 0 then everyone will have the same.

They could all start with 9 cents each. Boys could give the girls 1 cent and the girls could give the boys 1 cent ending up with the original 9 cents each.

Or every boy and every girl has 3 cent an the beginning. Every boy gives 1 cent to each girl. Now the boys are at zero, and every girl has 12 cent. The girls give 1 cent to every boy, and at the end everyone has 3 cent. So the answer is 3 cent at minimum.

Yes, I think Gerd's solution works and it is the best possible solution ignoring the trivial zero solution as the boys need to have a minimum of 3 cents each at the beginning.

The teaser, as of now, reads (emphasis is mine): -----

NINE boys and THREE girls agreed to share equally their pocket money. Every boy gave an equal sum to every girl, and every girl gave ANOTHER equal sum to every boy. Every child then possessed exactly the same amount. What was the SMALLEST POSSIBLE amount that each child then possessed? -----

The only correct answer to this teaser is that posted by Gizzer on Oct 09, 2002: they end up with 6 cents each. (jonnyonline overlooked the fact that 0 cents is not pocket money, and that "giving 0" is not giving).

NINE boys and THREE girls agreed to share equally their pocket money. Every boy gave an equal sum to every girl, and every girl gave ANOTHER equal sum to every boy. Every child then possessed exactly the same amount. What was the SMALLEST POSSIBLE amount that each child then possessed? -----

The only correct answer to this teaser is that posted by Gizzer on Oct 09, 2002: they end up with 6 cents each. (jonnyonline overlooked the fact that 0 cents is not pocket money, and that "giving 0" is not giving).

LOL I got it right but my reasoning was so wrong...does that mean its right?

Poorly worded.

It says that the girls give "another" equal sum, which I interpreted as a different sum. It said "and every girl gave another equal sum to every boy", so I assumed the exchange happened at the same time since it didn't say "then...".

So I got the answer 1--each boy started with 3 and each girl started with zero. Obviously the answer should be zero, not one.

It says that the girls give "another" equal sum, which I interpreted as a different sum. It said "and every girl gave another equal sum to every boy", so I assumed the exchange happened at the same time since it didn't say "then...".

So I got the answer 1--each boy started with 3 and each girl started with zero. Obviously the answer should be zero, not one.

Confusing. Apparently the teaser has been edited judging from the comments.

To post a comment, please create an account and sign in.

## Follow Braingle!