# 12 rubies weighing problem/riddle

• hussein236
In summary, a merchant has 12 identical rubies, one of which is either heavier or lighter than the rest. He has a balance scale and can only use it 3 times to determine which ruby is special and if it is heavier or lighter. The rubies are identical in shape but can be labeled, and the merchant has no other tools to use.
hussein236
i searched for this one if it is posted before, apparently not, but if it is, sorry for that.

a merchant has 12 identical rubies with equal masses that he wants to put on display, however, he knows that one of these rubies is special in the sense that its either heavier or lighter than the rest. he wants to know which one of them is the special one AND if it is heavier or lighter. however, he has a balance scale that he can use only 3 times. how would he identify the special ruby and know if its heavier or lighter.

notice:
the scale can only tell which side is heavier, the merchant can't measure the angle at which its sloped.
the rubies are of identical shapes, but they can be labeled.
the merchant doesn't have any other tools but the balance scale.

Fun stuff, this is.

Merchant weighs six rubies against six rubies. (2 weigh-ins remaining)
He takes the heavier six and divides them, three against three. He weighs these against each other. (1 weigh-in remaining)
The heavier three are split again. This time just one to one. (no weigh-ins remaining)
If the balance is not equal, the heavier one is obvious. If the balance is equal, then, by elimination, the last, unweighted ruby is the heaviest.

However, this only works if you know that the odd ruby is also the heaviest. I was just thinking about it and if, in the previous step, the balance is not equal and you don't know if the ruby is supposed to be heavier or lighter then you can't determine which the odd ruby is. I'd be very interested in hearing the solution if this is the case.

Last edited:
No

first move: 1234 x 5678

If 1234 lighter:

Second move 125 x 369

if 125 lighter

Third move 1 x 2

If 1 lighter: solution 1 lighter

If 1 heavier: solution 2 lighter

if equal: solution 6 heavier.

Second move: if 125 heavier
Third move: 5 x 12
5 heavier
equal 3 lighter

Second move: if 125 equal
Third move:7 * 8

If 7 heavier : 7
if 8 heavier : 8
if equal: 4 lighter

First move if 1234 heavier, same sequence but heavy light reversed.

First move if 1234 equal;
second move 9-10 x 11 - 1

9-10 heavier (lighter)

9 x 10

9 heavier (lighter)
10 heavier (lighter)
equal: 11 lighter (heavier)

Second move 9-10 equal

Third move 12 x 1
12 lighter of heavier

## 1. What is the "12 rubies weighing problem/riddle"?

The "12 rubies weighing problem/riddle" is a mathematical puzzle that involves using a balance scale to determine the weight of 12 rubies, with one of them being slightly lighter or heavier than the others.

## 2. How does the "12 rubies weighing problem/riddle" work?

The problem involves dividing the 12 rubies into three groups of four. Two groups are weighed against each other, with the third group kept aside. If the two groups weigh the same, then the odd ruby is in the third group. If one group weighs more than the other, then the odd ruby is in that group. This process is repeated until the odd ruby is found.

## 3. What is the purpose of the "12 rubies weighing problem/riddle"?

The purpose of the riddle is to test one's logical and analytical skills in finding a solution using limited information. It also helps in developing critical thinking and problem-solving abilities.

## 4. Is there a specific method to solve the "12 rubies weighing problem/riddle"?

Yes, there are various methods to solve the problem, such as the binary search method or the divide and conquer method. Each method involves dividing the rubies into groups and using the balance scale to eliminate possibilities until the odd ruby is found.

## 5. Can the "12 rubies weighing problem/riddle" be solved in a different way?

Yes, there are multiple ways to approach and solve the riddle. Some methods may be more efficient than others, but ultimately, the goal is to determine the odd ruby using the given information and the balance scale.

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