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Let us go into heroic fantasy land. The story
takes place in a antic land where dwarves are mining to extract gold.
The king is visiting the mine when he ears voices around the corner:
"I have a neat trick: we have to melt gold bars the size of this
mold, that is exactly 100 grams. I remove just a tiny fraction to all
my bars and they all weight 99 grams. Their scales are not precise enough,
they don't see anything..." The king tries to run after then, but
they ear him and manage to flee among the corridors. Annoyed, the king
summons the gods, who grant him a gift from the future: a digital scale.
The digital scales works as follows: you put whatever you want on the
scale, (nothing happens then), you press a button and the exact weight
of what is on the scale appears. Then, the scale vanishes. Note that
before you have pressed the button, no weight appears and once you have
pressed the button the weight won't change even if you add or remove
things. Armed with this mighty scale, the king summons all his 100 workers.
You should simply ask the first dwarf to put
one bar on the scale, the second dwarf, two bars, the third three and
so on. The missing number of grams will show the cheater. Note that
you could catch several cheaters by asking the n-th dwarf to put 2^n
bars... |
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