8 Balls

[thisiskyle]

Maybe you've heard this one before. It's considerably easier than the other one.

Let’s say you had eight balls and one was just slightly heavier than the other seven but, in all other ways, identical. How could you determine which ball was the heaviest using a scale (which allows you to make comparisons of weight: side A vs. side B) and making only two measurements.

[sonofobed]

This is a classic one that my High School Physics teacher posed us. I liked the logic behind the solution so much I never forgot it.

[lkelly2477]

Put 2 of the balls aside. Weight 3 of the remaining balls against the other 3 remaining. If they are the same then weigh the 2 balls that you put aside to find out which of them is heavier. If, instead, one of the sets of 3 balls was heavier, put one of the balls from the heavier set aside. Weigh the remaining two balls from the set to find out which one is heavier. If they are equal then you know it is the 1 ball that you put aside.

[Richard_BenoitEnglipedia Drone]

But what if the remaining sets of twos are not equal on your second measurement? How can you say with certainty which one of the two on the heavier side of the scale is the right ball?

[sonofobed]

Which remaining set of twos?

Step one: divide into 2 groups of three balls, and one group of two balls.

Step two: weigh the two groups of three balls, with three to each side.
If the scales are equal, then all 6 balls are equal weight and the heavy ball in the group of two you set aside.

If the scales are not equal, then the heavier side has the heavier mystery ball.

Step three: If the scales were equal in step two, split the group of two balls set aside earlier, and weigh each ball against the other, the heaver side being the mystery ball.

If the scales were not equal in step two, take the heavier group of three, one of these balls is the mystery one. Select at random two of the balls from the heavier group of three and weigh them against each other. If they are equal, then the remaining third, unweighed ball is the mystery ball. If the scales are unequal, then the heavier side is the mystery ball.

[sonofobed]

Also, when I heard this riddle it was 9 balls and not 8. Same strategy applies, just use three groups of three and proceed accordingly.

[Richard_BenoitEnglipedia Drone]

Weigh the remaining two balls from the set to find out which one is heavier. If they are equal then you know it is the 1 ball that you put aside.

Great explanation sono. I gots it. The above was what I read incorrectly. I thought it said:

"Weigh the remaining 2 balls from the sets."

[GETAK]

I'll try before I read other people's solutions:

Set aside 2 balls and compare the remaining 6. Put them on the scale in sets of 3 and 3.

-->If one group is heavier, set aside just those 3. Then set one ball aside and compare the remaining 2. If they're the same, the 3rd is the heavy ball.

-->However, if the original 2 groups of 3 are equal, just compare the 2 that you left aside at the beginning.