If you have 8 billiard balls, and one is defective meaning it weighs more....?

Question

How can you figure out the defective one in just two weighs?

Answer 1

Throw it aweigh?

Answer 2

this may be a little far fetched, but performed correctly it will work ,also it must be assumed you know the actual weight of a correctly fashioned ball...

step one .. Weigh all eight balls together

Step two.. Break each ball into 8 equal portions..
put 1 piece from the first ball 2 from the second 3 from the third and so on to eight pieces (or the whole ball) onto the scale all at once.

Step three.. Read the scale. (you should know the weight of a completely perfect ball so now you can determine the bad ball)

For example.. if an billiard ball weighs a perfect 8 pounds then 1/8th of a ball should weigh a pound and 8 balls should weight 64 pounds. First you weigh all 8 balls and it is 68 pounds. This means that the defective ball weighs an additional 4 pounds. since you put pieces that characterize each ball ( 1 from ball 1, 2 from ball 2 ect.) on the second weighing and you found its weight to be 37 pounds, you can now determine the answer.

An additional 4 pounds in one ball means that each of the sections (the ball was spilt into 8 pieces) of the defective ball must weigh 1.5 pounds instead of the usual 1 pound ((8+4)/8=1.5) since the pieces of balls we weighed came to 37 instead of 36 (1+2+3+4+5+6+7+8=36) then there was an extra pound. and since each piece of the defective ball weighed an extra 0.5 pounds, then there must have been 2 pieces which tells you which of the eight balls it was. It was the 2nd ball.


And i noticed other posters.. This is assuming you have a mass balance or scale. Not one of those two-sided scales where you can put a ball on both sides and check the BALANCE.. you said weigh so I stuck with actual weight.

Answer 3

Hmm

Select 6 balls at random and weigh them.

1. if they balance, then the defective one is left out. Remove the six, weigh the remaining 2 (one on each side) and the heavy side is defective.

2. if the original 6 do not balance, then you know the defective on is on the heavy side. Take the 3 balls from the heavy side, select 2 at random and weigh - if one side is heavier, it is the defective ball; if they balance the defective ball is the one leftover.

Either way, it's only 2 weighs.

Answer 4

split them into groups of 3, 3 & 2

first weigh the 3's ....
if they balance the remining two on each side will determine the heavy ball,,,
if they dont balance, take the group that weighs more and pick two.... if they balance the remaining is the heavy ball.. if they don't balancve...it's evident which is heavy