you have 9 marbles, they all weigh exactly the same.....?

Question

you have 9 marbles, they all weigh exactly the same except one weight slightly more, you are allowed to use a balance scale.
figure out which marble weighs more using the scale the least number of times possible

I. how many times you use the scale
II explaination

Answer 1

This is the clearest method I thought of.

Put any 4 marbles on both the pans of the scale. If the pans weigh equal, the left-out marble is the culprit. If one of the pans weigh heavier, take the 4 marbles out of that pan. Remove the other 4 innocent ones. Now put 2 of the suspect marbles on each pan. One is bound to be heavier. Take the the 2 marbles from that pan. Remove the other 2 innocent marbles. Now put 1 of the final suspects on each pan. You catch the culprit.

This method involves weighing 3 times. But you need to weigh only once if you find the culprit in the first step itself.

Answer 2

Allow me to quote my own site on this one: If you know that the odd marble is heavier than the others, you can detect it among up to 3^k marbles in just k weighing. So, 2 weighings are sufficient to find a heavier marble among 9.

A great related brain-teaser (discussed on the same page) is to detect an odd marble which could be heavier OR lighter than the others (you don't know which). This can be done for 13 marbles in just 3 weighings. With only 12 marbles you can even tell for sure if the odd marble is heavier or lighter than the rest (this is the classic way to pose that problem). If you're handed out one additional marble known to be good, you can even tell the bad marble from a heap of 14 (although you may not always be able to tell whether it's heavier or lighter).

For k weighings the maximum number of marbles which can be handled that way are respectively (3^k-3)/2, (3^k-1)/2 and (3^k+1)/2 (that's 12, 13 and 14 for k=3, as advertised above).

Give this (more challenging) puzzle a fair shot before peeking at the solution provided on this page of mine...

Answer 3

weighing twice is enuf.

Let the marbles be 1,2,3,4,5,6,7,8,9

first place 1,2,3 in left pan and 4,5,6 in the right pan of the balance.


if the left pan is heavier, then the heavier ball is either 1,2 or 3. For this, place 1 in left pan and 2 in right pan ... if any pan is heavier, solved .... or else 3 is the heavier marble.

if the right pan is heavier, then the heavier marble is either 4,5 or 6 .. use the same method as above to find which.

if both weigh equal, heavier marble is either 7,8 or 9. use the same method as above to find which.

Answer 4

Yeah the first answer is correct - dividing into three groups and weighing two will immediately determine the heaviest group, allowing you to quickly reduce the number from 9 to 3 to 1.

Answer 5

divide the marbles at 1-4-4
balance the 4-4
if the above eight marbles with equal weight,the remain is slightly more.

if one side of the marble is slightly more,
then repeat the procedure above to find the
slightly more one.

the minimum times to use the scale is 1
max. time is 3