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Crystal strength testing brainteaser

By David, 8 July 2020 Brainteaser

Difficulty: Taxing

Terri’s destructive testing lab is very popular. The most important piece of equipment is an electric-powered ram that smashes into samples to see how tough they are. It’s powered by capacitors, and by changing the number of capacitors that are plugged in, Terri can control how powerful the ram is.

Late in the day, a geologist knocked on Terri’s door. They had three identical crystals and wanted them to be tested by the ram.

Terri put the first crystal in place, connected 10 capacitors and fired the ram. The crystal shattered.

Terri now only has two crystals left to test with. The geologist wants to know the smallest number of capacitors that will smash the crystal. And there’s only time to run five more tests before the lab closes for the day.

Luckily, if a crystal survives a test, it will remain undamaged and can be reused.

Can you work out a plan for the remaining tests to get the work done in time?

For advanced mathematicians, can you make sure the testing takes fewer than five attempts?

Scroll down or click for a hint, or the answer!

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Brainteaser hint

If you could do 10 tests, which tests would you do? Remember, you have two crystals, so you can use one to get a ballpark, and the other to refine your guess.

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Brainteaser answer

One solution is to test a crystal with 5 capacitors:
• If it breaks, test the remaining crystal until it smashes, starting with 1 capacitor, then 2, then 3, then 4.
• If it doesn’t break, test the crystal again until it smashes, with 6 capacitors, then 7, then 8, then 9.

There’s actually a way to finish with only four tests! With the first crystal, try the following capacitor tests, stopping when the crystal breaks: 4, 7, 8, 9. Then, use the second crystal to refine your answer. For example, if it survives 4 and breaks at 7, then test 5 and 6.

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