Just had a cool idea: let's say that one wins by getting the medal and loses by perishing or having someone else get the medal, and all players want to win. From palyer 2's perspective, if he says "I don't know" and he's wearing a red hat, then you will win by following this video's reasoning. Moreover, if he's wearing a blue hat, you will also win with similar reasoning. Thus, saying "I don't know" has a 100% chance of losing to you, and player 2 will never say that if he's a good logician. He should instead bite the bullet and guess "blue" with a 67% winning chance. In fact, player 1 should never say "I don't know" for the same reason in this scenario.
At 0:08 I mention your friends are super smart haha! You are right with your friend trying to kill you however - I should have emphasized our assumption and made things more clear.. or maybe we should just get nicer friends.
Animations were great, explanation was simple yet complete. I really enjoyed this. The only thing was the paper background animation was a little distracting. Other than that, I loved it!!
Here’s a related (but mathematically unrelated) question. What are the odds for each player winning the game assuming they only answer with 100% certainty. Additionally, if they can only make 1 guess, what strategy can each player use to maximise their own chances of winning?
Here's how I came to the same conclusion. As person 1, I can reason as follows: 1. Everyone knows that the only way they can know the color of their own hat with no further information is if they see two blue hats. 2. Person 2 passes. That's no surprise. With 2 red hats visible to me, I know person 2 must pass, since he cannot see 2 blue hats. 3. Person 3 passes, which means (a) he does not see 2 blue hats (but we already know that), and (b) he realizes that person 2 did not see 2 blue hats. 4. Now person 3 knows either his hat is red or my hat is red. If my hat is blue, then person 3 would know that his hat must be red. But he doesn't know that or he'd say so. 5. Therefore my hat cannot be blue. It's red!
I really like this vid to challenge my ability to solve logic problems! Also, I think I might found another way to find out what is the color of the hat I'm wearing. Let's suppose in the room, there's a window or some sort of direct light, i could just make sure my hat is in the direct light's direction, bring my hand next to the hat and see what color is casting on my hand. Tadaaaaaaaaaaaaah, extremely safe guess.
You talk about risking which is misleading. What if first friend is bad at counting, and say pass while both you and second friend wear blue hats. Or what if second friend is not smart enough to come to conclusion he has red hat in case you would wear blue hat?
Just had a cool idea: let's say that one wins by getting the medal and loses by perishing or having someone else get the medal, and all players want to win. From palyer 2's perspective, if he says "I don't know" and he's wearing a red hat, then you will win by following this video's reasoning. Moreover, if he's wearing a blue hat, you will also win with similar reasoning. Thus, saying "I don't know" has a 100% chance of losing to you, and player 2 will never say that if he's a good logician. He should instead bite the bullet and guess "blue" with a 67% winning chance. In fact, player 1 should never say "I don't know" for the same reason in this scenario.
Great video!! Very interesting and amazing animations!
All sound unless "friend" #2 is either foolish, or, trying to get you killed.
At 0:08 I mention your friends are super smart haha! You are right with your friend trying to kill you however - I should have emphasized our assumption and made things more clear.. or maybe we should just get nicer friends.
This could be fixed by adding a single rule to the puzzle statement: Everyone dies if anyone guesses wrong.
Animations were great, explanation was simple yet complete. I really enjoyed this. The only thing was the paper background animation was a little distracting. Other than that, I loved it!!
Depends... are we moving at really high speeds? the blue hats might redshift to appear as red ones.
And also, you did not specify whether friend 2 knew that friend 1 was smart, because intelligence does not equal knowledge/information
Your videos are extremely underrated. The only thing I would wish for would be harder puzzles but I guess they will come in later videos.
Instructions unclear
Guessed the wrong hat and got sent to the void
Great video bud ;)
Here’s a related (but mathematically unrelated) question. What are the odds for each player winning the game assuming they only answer with 100% certainty.
Additionally, if they can only make 1 guess, what strategy can each player use to maximise their own chances of winning?
Great vid!
I want more videos like this! Great work
Here's how I came to the same conclusion. As person 1, I can reason as follows:
1. Everyone knows that the only way they can know the color of their own hat with no further information is if they see two blue hats.
2. Person 2 passes. That's no surprise. With 2 red hats visible to me, I know person 2 must pass, since he cannot see 2 blue hats.
3. Person 3 passes, which means (a) he does not see 2 blue hats (but we already know that), and (b) he realizes that person 2 did not see 2 blue hats.
4. Now person 3 knows either his hat is red or my hat is red. If my hat is blue, then person 3 would know that his hat must be red. But he doesn't know that or he'd say so.
5. Therefore my hat cannot be blue. It's red!
Can you give one more example of this...also great video bro all the best for SOMEpi win🎉
I really like this vid to challenge my ability to solve logic problems!
Also, I think I might found another way to find out what is the color of the hat I'm wearing.
Let's suppose in the room, there's a window or some sort of direct light, i could just make sure my hat is in the direct light's direction, bring my hand next to the hat and see what color is casting on my hand. Tadaaaaaaaaaaaaah, extremely safe guess.
You talk about risking which is misleading. What if first friend is bad at counting, and say pass while both you and second friend wear blue hats. Or what if second friend is not smart enough to come to conclusion he has red hat in case you would wear blue hat?
That’s exactly why I start out saying “your really smart friends”. Otherwise, just like you said, things become a lot more unpredictable :)