A man loans his friend his only 40 pound weight to weight grain on a balance scale. A week later the friend brings back the weight broken into 4 pieces. However, the man is happier now, because he can now measure anything weighing 1 to 40 lbs. (Note: the measured weights are in whole numbers. So he cannot measure 1.5 pounds.) What are the weights of each piece?

May 22 2006 06:25:53

Comments

if m right..its 1 , 3, 9 and 27

cheers

SS

May 22 2006 15:35:15

that doesnt sound right to me, I only say that because that combination would not allow you to weigh against an object that was two pounds.

May 27 2006 01:21:54

yes it would... add a 3 pound weight to one side.. the one pound weight to the other... then add whatever your weighing with the one pound weight... when it balances the item your weighing is two pounds...

~Dan

May 27 2006 05:33:02

1, 3, 9, and 27 is the only answer that works.

Some other answers are posted online... but no NOT work: 1, 9, 10, and 20... you cannot get 3 1, 2, 8, and 29... you cannot get get 4 7, 8, 10, and 15... you cannot get 19 and 5, 7, 8, and 20... you cannot get 9

BTW a 121 pound weight broken into 5 pieces will give you every integer up to 121. You'll need 1, 3, 9, 27, and 81

Aug 18 2009 17:54:34

i thought about

2, 5, 10, 20

but then i realized i cant get 38~40

Jun 21 2012 18:03:59

The weights are 4,6,12,22 permutations and combinations of these weights on the the balance scale covers all even numbers from 2 to 40 once the right combos for the range 2 to 40 are determined the odd numbers fall in between so when the balance scales shift between two consecutive even numbers the odd # is determined

Jul 10 2012 19:30:08

This is correct. I worked on this for 2 years, trying to find an algebraic solution. But to no avail. The LORD finally revealed the solution to me about 12 years ago. Of course the general solution are the powers of 3. But I still have not been able to find an algebraic solution. One of the weights has to be 1. You cannot get from 39 to 40 without a 1 pound weight. Also, you cannot get from 36 to 40 without a 3 pound weight and a 1 pound weight. Justin

cheers

SS

AnonymousSpyder~Dan

AnonymousSome other answers are posted online... but no NOT work:

1, 9, 10, and 20... you cannot get 3

1, 2, 8, and 29... you cannot get get 4

7, 8, 10, and 15... you cannot get 19

and

5, 7, 8, and 20... you cannot get 9

BTW a 121 pound weight broken into 5 pieces will give you every integer up to 121.

You'll need 1, 3, 9, 27, and 81

Anonymous2, 5, 10, 20

but then i realized i cant get 38~40

Anonymouspermutations and combinations of these weights on the the balance scale covers all even numbers from 2 to 40

once the right combos for the range 2 to 40 are determined the odd numbers fall in between so when the balance scales shift between two consecutive even numbers the odd # is determined

AnonymousAnonymous