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Imagine that you had 12 coins. One of the coins, being fake, weighs less than the other 11. You have one balance that will break if you make more than 3 measurements. How do you determine which coin is fake?
(Inspiration for this comes from http://www.scientificpsychic.com/mind/mind1.html)
How is this relevant? Experiments (and anything, really) cost time and money. In order to be a good steward of the resources we are given, it is important to minimize waste and unnecessary experiments. Sometimes, due to the amount of time required to do an experiment, you can only do a certain number of experiments before a deadline. You also have a limited budget. Similarly, when making a product, you want to keep the production costs low, so you don't want to do excessive experiments and tests that add to the product cost without really improving product quality.
An answer is given in the comments section.
Can you go further? Try finding the one fake coin in a bag of 18 coins.
In my solution:
ReplyDeleteMeasurement 1: Put 4 coins in the left side of the balance and 4 coins in the right side. If one side weighs less, the fake coin is on this side. If the two sides weigh the same amount, the fake coin is in the 4 coins that you have not weighed yet.
Measurement 2: Remove all coins from the balance. Of the grouping of four that contained the fake coin, put 2 coins on one side of the balance and put the remaining two on the other side. The fake coin is located on the lighter side.
Measurement 3: Remove all coins from the balance. Of the 2 coins that were on the lighter side, put one coin on one side of the balance and the other on the other side. The lightest of these two is fake.