How can you identify a defective machine with only one use of a scale?

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The discussion revolves around a classic problem involving ten coin-producing machines, where one machine is defective and produces coins that are 10% lighter than the others. The challenge is to identify the defective machine using a scale only once. A hint is provided, suggesting a numerical approach, specifically referencing the sum of the first three integers. Participants share their experiences with similar problems, including a related puzzle about groups of balls with varying weights. The conversation highlights the importance of creative problem-solving and numerical strategies in tackling such puzzles.
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I am sure this one has been done a million times, but I can't figure this out. It about 10 mint producing machine and one of them is defective and produces coins that weigh 10% less than the other 9. You have a scale but you can only use it once and only once, how would you identify the defective machine?
 
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What have you tried?
 
Here's a hint: What's 1+2+3?
 
This puzzle has been presented in a slightly different form in the thread entitled: inspector Columbo.
 
I solved another problem of same kind, which says there are 10 groups of 10 balls each and each ball in a group weighs 10gms except one group which has 9 gm balls in it, by an excellent case of coincidence.

When I was in school I had a grave problem with my third language and only way out for me is to mug up. I often used to forget part of the essays and poems, so my teacher advised me to count numbers to calm down myself and try remembering them. I was totally baffled when the above problem was given to me and started counting numbers. I got that when I reached 10.
 
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