Ten Jars, One of Them Light
The puzzle
You have ten jars of pills. In nine of them every pill weighs 10 grams. In one jar - you do not know which - every pill weighs 9 grams.
You have a digital scale that gives an exact reading, and you may use it exactly once. Which jar is the light one?
Stuck?
One at a time, smallest first. Open only as many as you need — the whole point of the puzzle is the part you work out yourself.
Hint 1
You are allowed to take as many pills as you like from each jar, and to mix them on the scale.
Hint 2
If each jar contributes a different number of pills, what does the shortfall from the expected weight tell you?
Show the answer Hide the answer
Take one pill from jar 1, two from jar 2, and so on up to ten from jar 10, and weigh all fifty-five together. The number of grams short of 550 is the number of the light jar.
How to get there
Number the jars 1 to 10 and take that many pills from each: one from jar 1, two from jar 2, up to ten from jar 10. That is 1+2+...+10 = 55 pills.
If every pill weighed 10 grams the pile would weigh 550 grams. Each light pill is one gram short, and the number of light pills in the pile is exactly the number of the light jar.
So weigh the pile once. A reading of 547 grams is three grams short, which means three light pills, which means jar 3. A reading of 543 means jar 7.
The technique worth keeping
One weighing looks like one number, and one number looks like it cannot separate ten cases - until you make each case contribute a different amount to it. Taking a distinct count from each jar turns a single reading into an address.