26 Stones and 3 Scales?

Question

I have 26 stones which are all identical, save one has a chunck of gold in the center and weighs slightly more than the rest.

I have 3 balances, each of which I can only use once.

How can I find the stone with the gold?

I saw the same question asked about 12 stones so I decided to kick things up a notch. You can actually do even more stones than 26.

Good luck!

Answer 1

Seperate the stones into two groups of nine stones and one group of eight stones.

Balance the two groups of nine stone. If they balance, the group of eight contains the heavy stone. If they do not, the heavier group of nine contains the heavy stone.

Find the heavier group and seperate it into three groups of three stones each. (If the eight-stone group contains the heavy stone, you can add one stone from either of the first groups to make three even groups. Or not. It works either way). Balance two of the groups. If they balance, the heavy stone is in the unweighed group of three, otherwise it is in the heavier group.

Find the heavy group of three and balance two stones out of it. If they balance, the heavy stone is the one you left out. If they do not, obviously, the gold is in the heavier of the two stones.

Answer 2

split them into two groups of 9 and one group of 8.

weigh the two groups of 9 together

Case 1, they are equal) then you know the gold is in one of the other 8. Split this into two groups of three and one group of two and place the two groups of three on either side of the balance.

Case 1.1, they are equal) Then you know that it is one of the last two. place these two on either side of the balance. the one that weighs more has the gold.

Case 1.2, the second weigh is not equal) Then one side weighs more, and the gold is on that side. Now take the two from the side that weighs more and place them on the balance. If they don't balance, the one that weighs more has the gold. If they do balance then the last one has the gold.

Case 2, the first weigh doesn't balance) Then you know it is the group that is heavier. Break this into 3 groups of 3 and put two groups on the balance.

Case 2.1 they balance) then you know it is one of the three that wasn't on the balance. Place two of them on the balance, if they balance than it is the third. If they don't balance, then it is the heavier one.

Case 2.2 they don't balance) then you know that it is one of the heavier one. place two of the three from the heavier side on the balance. If they balance, then it is the third. If they don't, then it is the heavier one.

Answer 3

seperate into a pile of 9, 9, and 8
weigh the two piles of 9
if the scales are even your gold is in the pile of 8
otherwise the gold is in the heaviest pile

now you have a pile of either 8 or 9 to examine
seperate this into a pile of 3, 3, and either 2 or 3
weigh the two piles
again, if the scales are even your unwieghed pile has the gold
otherwise its the heavier of the two

you now have a pile of either 3 or 2
if you only have 2, the heaviest is the gold
otherwise weigh two and leave one out
of one is heavier it has the gold
if they are even the one left out is the gold

...darn, two people beat me =(

Answer 4

In general it's the same solution as with 12 stones.
scale 1: you divide the stones to three groups of 9,9 and 8 stones
and you weigh the two group with 9 stones. If they are identical than the gold is in the third group otherwise it's in the heavier group

scale 2: again we divide the selected group into three group (3,3,3 or 3,3,2) and again we weigh two groups of 3 stones.If they are identical than they gold is in the third group otherwise its in the heavier group.

Scale 3: now we are left with either three stones or two. if we are left with two than we simply compare than to find out which one is heavier. If we are left with three stones than again we randomly compare two stone, if they are identical than the gold is in the third stone otherwise the gold is in the heavier stone.

Answer 5

I've heard something similar with 12 golf balls....don't know how to figure it out but its been wracking by brain since, I'm probably thinking too hard about it, but i would love to know how to do either

Answer 6

can use 9 by just two balances
???????