Can You Detect the Counterfeit Coins?
Image: Photo: Shutterstock Graphics: Vicky Leta
Welcome to the first Gizmodo Monday Puzzle, a new series in which I will pose thought-provoking challenges at the beginning of every week to jumpstart your brain. I am a lifelong puzzle lover, sometime puzzle creator, and new Gizmodo puzzle writer. Many of the teasers posted here will be difficult—but they will be solvable by the persistent among you, without the need for specialized knowledge or higher-level math. Some will be classics from the puzzle world, and many will be lesser-known gems. They will not be gimmicky, meaning that what the puzzle seems to be asking really is what it is asking. And finally, they will be influenced by you! If you know a great puzzle that you think should be covered here, send it my way: firstname.lastname@example.org.
To kick off the series, I’ve chosen an old favorite in which you will try to avoid being ripped off by making clever use of a scale. It hits the sweet spot, difficulty-wise. The solution will not be immediately obvious to most people, and yet if you chew on it for a little while, clarity will come. Discuss your thoughts openly in the comments section, but be warned that spoilers might lurk there. If you’ve heard this puzzle before, I ask that you not post the solution and instead give a fresh solver a chance to be first. Good luck!
Puzzle #1: 10 Bags of Coins
You have 10 bags; each bag contains 10 coins. In nine of the bags, every coin weighs exactly 1 gram. However, one of the bags holds counterfeit coins, which weigh 1.1 grams apiece. You don’t know which bag contains the false coins, and the weight difference is too subtle to feel with your hands. Luckily, you have a scale to help. It displays a precise and accurate numeric readout (for example, if you placed a raisin on the scale, it might display: “.58 grams”). Not so luckily, the scale’s battery is dying and after one use it will conk out. How can you identify the bag with the heavier coins using only a single weighing on the scale? You are allowed to take coins out of their bags, but you only get to read one number from the scale.
Like many great puzzles, this sounds impossible at first. How can a single number provide enough information to find 10 fake coins out of 100? However, there is a beautiful and gimmick-free solution that is just a stroke of insight away.
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We will post the solution next Monday, along with a new puzzle!
Special thanks to Robbie Gonzalez, who previously and deftly helmed a weekly puzzle at Gizmodo. I was a big fan of that column and hope that this new incarnation is just as fun and stimulating.