The gold bars

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.

How will he find the cheater?






 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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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