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

  • Thread starter Sakha
  • Start date
In summary, the dwarves came up with a plan to ensure that 9 of them would survive the giant's challenge of guessing the color of their hats correctly. They used their positioning and the fact that they can only say "White" or "Black" to guarantee that 9 of them would get it right. The last dwarf, however, had a 50-50 chance of survival. This plan was devised to counter the control that the giant held over the dwarves.
  • #1
Sakha
297
0
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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  • #2
Is the giant a black hole?
 
  • #3
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:
  • #4
Each of the 10 told the color of the hat on the one directly in front.
 
  • #5
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.
 
  • #6
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.
 

1. What is the significance of 10 dwarves and a giant?

The phrase "10 dwarves and a giant" is often used as an analogy or metaphor to represent a situation where a group of smaller, weaker individuals are faced with a larger, more powerful individual or entity.

2. Is there a scientific basis for the concept of dwarves and giants?

No, the concept of dwarves and giants is primarily found in folklore and mythology, and does not have a scientific basis.

3. Are there any real-life examples of "10 dwarves and a giant" situations?

There are many examples of "10 dwarves and a giant" situations in various contexts, such as in sports where a smaller team or individual competes against a larger and more dominant opponent.

4. Can the outcome of a "10 dwarves and a giant" situation be predicted?

It is difficult to predict the outcome of a "10 dwarves and a giant" situation, as there are many factors that can influence the outcome, including strategy, skill, and luck.

5. How can individuals in a "10 dwarves and a giant" situation overcome the odds?

Individuals in a "10 dwarves and a giant" situation can increase their chances of success by working together, utilizing their strengths, and finding creative solutions to counter the advantages of the larger and more powerful opponent.

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