self Maths Puzzle

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?

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self Other Question

Two trains are 200 km apart, and travelling towards each other at 50 km/hour each.

From one train a fly takes off, flying straight above the rails to the other train at the speed of 75 km/hour, bounces off it and flies back to the first train.

This is repeated till the trains crash together and the fly is smashed (Headline: Fly Dies in Freak Train Crash)

What distance is the fly able to fly until its meet its tragic end?

Note: there is a complicated and an easy way to solve this one. 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?