A FEW BRAINTEASERS

You are given 50 tiny steel balls and a small, but very exact, balancing scale.
Each of the balls weighs 15 grams, with only one weighing 2 grams more than the rest.
Can you, by using the scale only four times, find and isolate this oversized steel ball?
What number?

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What is the next number in this row of numbers?
484, -576, 529, ...

The King of Persia

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The checkerboard has 64 squares. Legend tells us that it was designed in ancient times by a Persian and that his king was so delighted with the new game that he promised the inventor any gift he should wish as a reward (perhaps excluding the royal princess).
Well, said the chess master, he would like for the king to put one grain of barley on the first square, two on the next, four on the third, then eight, and so on.
The king was astounded. Was that really all he wanted?
Only later did the king find out that there wasn't that much barley in the royal granaries, nay in all the granaries of Persia if not the granaries in all of the known world.
How big a pile of barley would be on the 64th square, roughly?
.....
That, incidentally, equals the number of your direct male and female ancestors if you travel 64 generations back in time, or about to the time of the beginning of the Christian era.

  You're saying?

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What comes once in a minute, twice in a moment, but never in a thousand years?

  Machinery

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'One machine can do the work of fifty ordinary men. No machine can do the work of one extraordinary man.' (Elbert Hubbard)