Math and Arithmetic

Algebra

# Out of 9 balls 8 balls weight the same 1 is lighter. using scales twice which ball is lighter?

###### Wiki User

###### 2008-08-28 00:47:33

Set three balls aside. Divide the remaining 6 balls into 2

groups of 3 and **weigh** them. If the groups weigh the same,

the lightest ball must be in the group you set aside. Otherwise,

the lightest ball is in the group that weighed less. Take the group

of thee that remains and set aside one ball. **Weigh** the other

two. If the two balls weigh the same, the lightest ball must be the

one you set aside. Otherwise, the lightest ball is the one that

weighed less.

## Related Questions

###### Asked in Brain Teasers and Logic Puzzles, IQ

### There are nine balls and a balance not a scale One of the balls is lighter than the rest How do you find the lighter ball by using the balance only twice How do you do it?

First balance Divide the balls into three groups of
three. Put two groups on the balance, three balls per side. If they
balance, the lighter ball in the third group. If one group is
lighter (that side of the balance is higher), it's in that group.
(You have determined which group of three the lighter ball is in,
and now identify it with a second use of the balance.) Second
balance Take any two of the balls from the group of
three that contains the light ball and put them on the two sides of
the balance. If they balance, it's the third ball. If they don't,
it's the one that's higher in the air.

###### Asked in Science, Physics, IQ, Verbs

### How can you tell which of three balls is the lightest or heaviest using a simple balance that consists of two pans?

Tough question to get into one sentence! You can do it in two
weighings. Select any two of the balls and place one on each pan.
If the scale balances, the third ball is the oddball. A second
comparison will determine whether the oddball is lighter or heavier
than the other two balls. Simply replace one of the first two balls
with the oddball. If the oddball is heavier, its pan will drop; if
it's lighter, its pan will rise. But what if the scale fails to
balance the first time? (It is twice as likely that the scale will
fail to balance when selecting two of the three balls at random for
the first comparison!) If the scale fails to balance on the first
comparison of two randomly selected balls, then you know that the
oddball is on the scale, but you do NOT know which one it is, and
you don't know whether it's heavier or lighter than the other two.
A second comparison will resolve those issues. Remove the lighter
ball from its pan and replace it with the third ball. If the scale
remains out of balance, then you know that the heavier ball is the
oddball, which is, of course, heavier than the other two. If,
however, the scale balances, then the ball you removed is the
oddball and is lighter than the other two.