12 rubies weighing problem/riddle

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 cant measure the angle at which its sloped.
the rubies are of identical shapes, but they can be labeled.
the merchant doesnt have any other tools but the balance scale.

FLFisherman

Fun stuff, this is.

Spoiler

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.

Andre

No

Spoiler

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

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