How did the dwarves outsmart the giant's deadly hat game?

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SUMMARY

The dwarves devised a strategic plan to survive the giant's deadly hat game, ensuring that 9 out of 10 would definitely live. The last dwarf, who could see the hats of the 9 in front, would announce the color of his hat based on the parity of the number of black hats he observed. If he saw an even number of black hats, he would declare his hat as white; if odd, he would declare it as black. This method guaranteed that the remaining dwarves could deduce their own hat colors based on the previous dwarf's declaration and the hats they could see.

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10 dwarves where hanging around and a big giant came, he said that tomorrow he will put them on a column, each of them facing forward. He will put them white and black hats, and ask from the last to the first which color is his hat, if one told it right, he live, if not he die. The dwarves had a night to make a plan, and they made a plan that 9 of the dwarves would 100% live, and the last one had 50-50.

What was this plan?

Some stuff to know:
They can only say White or Black.
They're all facing forward, so the last one can see all the 9 hats of his friends, and the 9th could see all the 8 hats, and so on.
 
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Is the giant a black hole?
 
They can decide to pronounce white/black differently depending upon what's the color of next dwarf hat.

If the next dwarf has white then take longer time to say your hat color and if it is black say it faster.
 
Last edited:
Each of the 10 told the color of the hat on the one directly in front.
 
Assign 0 to white and 1 to black (for instance). The first one (last in the row) sees all other hats, adds all the numbers, and says b or w according to the parity of the sum of other hats. 50/50% will it match his own hat. Later on, the next in the line can deduce the color of his own hat, by the knowledge of all hats in front of him.
 
rootX said:
They can decide to pronounce white/black differently depending upon what's the color of next dwarf hat.

If the next dwarf has white then take longer time to say your hat color and if it is black say it faster.
Thats a way, but what we want is a real logical answer. Thats why its with giant and dwarves, to state the control the giant has over the dwarves.
jimmysnyder said:
Each of the 10 told the color of the hat on the one directly in front.
What if the one on your back tells you're black, and the guy in front of you is white, will you save yourself or the one in front of you.
humanino said:
Assign 0 to white and 1 to black (for instance). The first one (last in the row) sees all other hats, adds all the numbers, and says b or w according to the parity of the sum of other hats. 50/50% will it match his own hat. Later on, the next in the line can deduce the color of his own hat, by the knowledge of all hats in front of him.
Yep you got it.
The exact answer:
The last one says white if he looks a even number of blacks, and the others deduce from it and keep it going.
 

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