SOLUTION: ok. i've got a tough one. A man selling fruit has only three weights, but with them he can weigh any whole number of kilograms from 1 kg up to 13 kg inclusive on his balance. wh

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: ok. i've got a tough one. A man selling fruit has only three weights, but with them he can weigh any whole number of kilograms from 1 kg up to 13 kg inclusive on his balance. wh      Log On


   

Question 163599: ok. i've got a tough one.
A man selling fruit has only three weights, but with them he can weigh any whole number of kilograms from 1 kg up to 13 kg inclusive on his balance. what weights does he have?
please HELP!!!
Answer by J2R2R(94) About Me  (Show Source):
You can put this solution on YOUR website!
The easiest way to look at this instinctively is to realise that you don’t just ‘add’ weights to weigh; you can ‘subtract’ weights by placing them on the other side.

If you could only add weights you could have to use 1, 2, 4, etc. as in binary which can represent any integer using 0s and 1s. 1, 1+0, 1+1, 1+0+0, 1+0+1, 1+1+0, 1+1+1 etc. as we are adding all the time.

Number, add = 2 degrees of freedom.

But as you can also subtract (putting weights on the other side), you can use the powers of 3 instead of 2 which gives us 1, 3 and 9 to make 13. Subtracting gives us an extra degree of freedom so we can advance in powers of 3.

Number, add, subtract = 3 degrees of freedom

1, 3-1, 3, 3+1, 9-3-1, 9-3, 9-3+1, 9-1, 9, 9+1, 9+3-1, 9+3, 9+3+1

So, how do we subtract a weight – easy, just put it on the side of the item you are weighing.

E.g. to weigh something of 6 kg, you would place 9 kg on one side and 3 kg on the side with the object you are trying to weigh. When they balance you know the object you are weighing is 6 kg.

So the answer is 1 kg, 3 kg and 9 kg.