self Maths Puzzle

You have 10 bags full of coins, in each bag are 1,000 coins.

But one bag is full of forgeries, and you can't remember which one.

But you do know that a genuine coins weigh 1 gram, but forgeries weigh 1.1 grams.

To hide the fact that you can't remember which bag contains forgeries, you plan to go just once to the central weighing machine to get ONE ACCURATE weight.

How can you identify the bag with the forgeries with just one weighing?

And what if you didn't know how many bags contain forgeries?

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self Other Question

Three out of six look-alike balls are heavy. The other three are light.

How many weighings on a beam balance are necessary to identify the heavy balls?
ou have 9 balls, equally big, equally heavy - except for one, which is a little heavier.

How would you identify the heavier ball if you could use a pair of balance scales only twice?