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The hundred hat riddle

Deepak Kiran

Paw Patrol of ZoZo
Posting Freak
100-hat-riddle.jpg

1. 100 prisoners stand in line, one in front of the other, each wearing either a red hat or a blue hat.

2. Every prisoner can see the hats of the people in front but not their own hat, or the hats worn by anyone behind.
3. A prison guard starts at the back of the line and asks each prisoner the colour of their hat. If they answer correctly, they will be pardoned, if they get it wrong, they’ll be executed.

4. Before lining up, the prisoners are allowed to collectively come up with a strategy.

The good news is, there IS a way for 99 of the prisoners to definitely survive and the remaining prisoner to have a respectable shot at 50 per cent.

  • To get this result, the first prisoner in the line must say "blue" if he sees an even number of hats in front of him.
  • If he sees an odd number of hats in front of him, he must say "red".
  • This information, coupled with the responses other prisoners have already given and the hats in front is enough to work out what colour hat is on your head.
So, everyone except the first prisoner will definitely answer correctly
 
View attachment 12078

1. 100 prisoners stand in line, one in front of the other, each wearing either a red hat or a blue hat.

2. Every prisoner can see the hats of the people in front but not their own hat, or the hats worn by anyone behind.
3. A prison guard starts at the back of the line and asks each prisoner the colour of their hat. If they answer correctly, they will be pardoned, if they get it wrong, they’ll be executed.

4. Before lining up, the prisoners are allowed to collectively come up with a strategy.

The good news is, there IS a way for 99 of the prisoners to definitely survive and the remaining prisoner to have a respectable shot at 50 per cent.

  • To get this result, the first prisoner in the line must say "blue" if he sees an even number of hats in front of him.
  • If he sees an odd number of hats in front of him, he must say "red".
  • This information, coupled with the responses other prisoners have already given and the hats in front is enough to work out what colour hat is on your head.
So, everyone except the first prisoner will definitely answer correctly
:hitthewall:
 
View attachment 12078

1. 100 prisoners stand in line, one in front of the other, each wearing either a red hat or a blue hat.

2. Every prisoner can see the hats of the people in front but not their own hat, or the hats worn by anyone behind.
3. A prison guard starts at the back of the line and asks each prisoner the colour of their hat. If they answer correctly, they will be pardoned, if they get it wrong, they’ll be executed.

4. Before lining up, the prisoners are allowed to collectively come up with a strategy.

The good news is, there IS a way for 99 of the prisoners to definitely survive and the remaining prisoner to have a respectable shot at 50 per cent.

  • To get this result, the first prisoner in the line must say "blue" if he sees an even number of hats in front of him.
  • If he sees an odd number of hats in front of him, he must say "red".
  • This information, coupled with the responses other prisoners have already given and the hats in front is enough to work out what colour hat is on your head.
So, everyone except the first prisoner will definitely answer correctly
Dk where is the answer:map:
 
There is no definite answer, it's a probability calculation. Utmost 99 can be found.
 
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