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

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Discussion Overview

The discussion revolves around a logical puzzle involving dwarves and a giant, where the dwarves must deduce the color of their hats based on the visibility of others' hats and a strategic plan to maximize their survival. The scope includes logical reasoning and problem-solving strategies.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant describes a scenario where 10 dwarves must identify the color of their hats, with a plan that ensures 9 will survive while the last has a 50-50 chance.
  • Another participant questions the nature of the giant, suggesting a metaphorical interpretation as a black hole.
  • A further response emphasizes the need for a logical answer, indicating that the scenario is designed to illustrate the control the giant has over the dwarves.
  • Participants discuss the implications of the information shared by the dwarves regarding their hat colors and the decisions made based on that information.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the giant's role or the logical strategy to be employed, indicating multiple competing views and unresolved aspects of the puzzle.

Contextual Notes

The discussion lacks a detailed breakdown of the proposed logical strategy, and assumptions about the visibility and communication between the dwarves remain unexamined.

Sakha
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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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