# Factory That Produces Dumbbell Weights

You work at a factory that produces dumbbell weights for lifting. One of the 10 machines has been producing weights that are always 1 pound less than the rest of the machines. You have a large scale used to weigh the weights for quality control.

How could you find the defective machine by using the scale only once?

You are allowed to make as many weights with the machines as you please.

### 3 guesses to Factory That Produces Dumbbell Weights

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• Frank

Take 1 weight from machine 1, 2 from machine 2, 3 from machine 3….etc to 10 from 10.

If your total expected weight is light by 1 lb it is machine 1, if it is light by 2 lbs, it is machine 2, etc.

• Borrow one dumbbell from the first machine, two from the second, three from the third, and so on (you can actually SKIP the tenth machine altogether). Determine what the total weight SHOULD be, then use the scale to see what the total actually is. The difference between those two numbers will be the same as the machine from which you borrowed that many dumbbells (for example, if the total is nine pounds off then the faulty machine is the ninth one). And lastly, if there is no difference between what the total weight should be and what it actually is then the problem machine must be the 10th machine, the one you did not include.

• Frank, you are the winner!
From each machine you make a different number of weights and however many pounds the scale is off from what it should be corresponds to the machine that made that many weights. From machine 1 you make 1 weight, machine 2 you make 2 weights… If the machine is off by 1 pound you know it was machine 1 that was off.