Brainteaser #28 – Sapphires and Rubies

brainteasers

You work at a gemstone production facility.

One day, you’re with your colleague at the conveyor belt when suddenly, a system failure causes the boxes of gemstones to be labelled incorrectly.

Your colleague stops the machine and shows you 3 boxes. One is labelled S, for sapphires, one is labelled R, for rubies, and the other is labelled SR, for a mixture of both.

Your coworker says that you can pick one box, and they will pull out a gemstone and show you. You can only do this once.

Can you work out what gemstones are in what boxes from this ONE choice?

Remember, the boxes are all 100% incorrectly labelled.

Show Answer

To solve this, you simply ask your colleague to remove a gemstone from the SR box.

This box is incorrectly labelled, like the others.

If your colleague pulls out a sapphire, you know the box is full of sapphires only. If they pull out a ruby, you know it is only rubies.

Why? Because we know it isn’t true to its label of SR. It cannot be a mix, it can only be one or the other gemstone.

Now you know that the SR box is either sapphires or rubies, you can work out the other boxes easily.

Say your colleague removes a sapphire from the SR box, this means that the box labelled R must have rubies and sapphires in it, as you know it cannot only have sapphires (as you identified that box already), and it cannot have just rubies as it’s labelled incorrectly. This means SR is sapphires, R is rubies and sapphires and S is rubies.

If they pulled out a ruby first then SR would be rubies, R is sapphires and S is rubies.

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