Poor Taylor #1 : I got conned
Yes.... she got conned.... that's bad news.
She bought diamond rings yesterday, one of them which is fake.
She's going crazy! Help her.
At least how many times will she have to use a 2-sided scale (assume it can hold an large amount of mass) to find out which ring is fake?
[All stories are made-up, not real. Don't take it too seriously ;)]
The answer is 2017.
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First, divide the pile of rings to 3 parts, that is, 3 2 0 1 6 rings in each category.
Then, place two of the batches of rings each on one side of the scale.
If any one of the sides is slightly higher than the other, the fake ring is inside. If it comes to a perfect balance, the fake ring is in the other batch.
Next, repeat the steps again again and again.....
Take 9 rings ( 3 2 ) as an example. This number requires a minimum amount of 2 tries. As for 27, 3 tries is the minimum requirement.
In general, for 3 x number of rings, x tries are required at least to find out the fake ring.
[Hint: You may want to try with a smaller number before attempting large scale numbers like 3 2 0 1 7 ]