You are sitting at a table that has a whole bunch of coins scattered on it. You notice that exactly ten of these coins are tails up. All of a sudden, all the lights in the room go out and it's pitch black.
The question: how can you make two stacks of coins so that you can guarantee that each stack has the same number of coins tails up? Note that, in the dark, you cannot tell one side of a coin from the other - ie, they feel/taste/smell/etc the same on each side.
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
After losing a battle to his rival, an angry king decided that he would execute the 50 engineers he had in his employment. He marched them out on the field and prepared to execute them, but at the last second, the king felt pity and decided to give them one last chance to live.
The king explained to the engineers that on the following day, the 50 engineers would again be marched out onto a field. They would stand in a straight line, back to front, all facing the same direction, so each man sees just the backs of the men in front of him. The king's soldiers would then put, at random, either a red or black hat on each engineer. The engineer would be able to see all the hats of the men in front of him, but not his own or those of the men behind him.
The king would then start at the back of the line - that is, the engineer who can see the other 49 engineers in front of him - and ask: "is your hat red or black?" The engineer would then answer with one word: either "red" or "black". If he gets it right, he lives. If he gets it wrong, he is immediately executed. Either way, the king moves up the line asking the same question to each engineer in turn. If an engineer says anything other than "red" or "black" or if any of the engineers cheat (try to look at their own hats), all 50 are immediately executed.
Question: what strategy can the engineers come up with to guarantee the maximum number of them survive?
Originally posted by: brikis98
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
correct. had you heard this one before, use google or did you actually figure it out?
(personally, this one took me a LONG time to get)
Originally posted by: Aikouka
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
After a quick look at that, I don't think it works. For example, if I place 1 coin into the one group and 99 into the other group, do you think I'll have only 1/99 coins tails up? Especially when there were 10 to begin with!
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
I believe in MotionMan's answer, he means that N = 10, or whatever number was initially tails up...
Originally posted by: brikis98
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
correct. had you heard this one before, use google or did you actually figure it out?
(personally, this one took me a LONG time to get)
Originally posted by: brikis98
To keep this thread going, I'll add one more, but I hope someone else has something for the future:
After losing a battle to his rival, an angry king decided that he would execute the 50 engineers he had in his employment. He marched them out on the field and prepared to execute them, but at the last second, the king felt pity and decided to give them one last chance to live.
The king explained to the engineers that on the following day, the 50 engineers would again be marched out onto a field. They would stand in a straight line, back to front, all facing the same direction, so each man sees just the backs of the men in front of him. The king's soldiers would then put, at random, either a red or black hat on each engineer. The engineer would be able to see all the hats of the men in front of him, but not his own or those of the men behind him.
The king would then start at the back of the line - that is, the engineer who can see the other 49 engineers in front of him - and ask: "is your hat red or black?" The engineer would then answer with one word: either "red" or "black". If he gets it right, he lives. If he gets it wrong, he is immediately executed. Either way, the king moves up the line asking the same question to each engineer in turn. If an engineer says anything other than "red" or "black" or if any of the engineers cheat (try to look at their own hats), all 50 are immediately executed.
Question: what strategy can the engineers come up with to guarantee the maximum number of them survive?
Originally posted by: brikis98
To keep this thread going, I'll add one more, but I hope someone else has something for the future:
After losing a battle to his rival, an angry king decided that he would execute the 50 engineers he had in his employment. He marched them out on the field and prepared to execute them, but at the last second, the king felt pity and decided to give them one last chance to live.
The king explained to the engineers that on the following day, the 50 engineers would again be marched out onto a field. They would stand in a straight line, back to front, all facing the same direction, so each man sees just the backs of the men in front of him. The king's soldiers would then put, at random, either a red or black hat on each engineer. The engineer would be able to see all the hats of the men in front of him, but not his own or those of the men behind him.
The king would then start at the back of the line - that is, the engineer who can see the other 49 engineers in front of him - and ask: "is your hat red or black?" The engineer would then answer with one word: either "red" or "black". If he gets it right, he lives. If he gets it wrong, he is immediately executed. Either way, the king moves up the line asking the same question to each engineer in turn. If an engineer says anything other than "red" or "black" or if any of the engineers cheat (try to look at their own hats), all 50 are immediately executed.
Question: what strategy can the engineers come up with to guarantee the maximum number of them survive?
Originally posted by: JS80
Originally posted by: brikis98
Originally posted by: MotionMan
Place any N coins into one group and the remaining coins into the other
group.
Flip over over all N coins in the first group.
I don't have a new one, so someone can take my turn.
MotionMan
correct. had you heard this one before, use google or did you actually figure it out?
(personally, this one took me a LONG time to get)
can you explain this i don't even get it
Originally posted by: JS80
Originally posted by: brikis98
To keep this thread going, I'll add one more, but I hope someone else has something for the future:
After losing a battle to his rival, an angry king decided that he would execute the 50 engineers he had in his employment. He marched them out on the field and prepared to execute them, but at the last second, the king felt pity and decided to give them one last chance to live.
The king explained to the engineers that on the following day, the 50 engineers would again be marched out onto a field. They would stand in a straight line, back to front, all facing the same direction, so each man sees just the backs of the men in front of him. The king's soldiers would then put, at random, either a red or black hat on each engineer. The engineer would be able to see all the hats of the men in front of him, but not his own or those of the men behind him.
The king would then start at the back of the line - that is, the engineer who can see the other 49 engineers in front of him - and ask: "is your hat red or black?" The engineer would then answer with one word: either "red" or "black". If he gets it right, he lives. If he gets it wrong, he is immediately executed. Either way, the king moves up the line asking the same question to each engineer in turn. If an engineer says anything other than "red" or "black" or if any of the engineers cheat (try to look at their own hats), all 50 are immediately executed.
Question: what strategy can the engineers come up with to guarantee the maximum number of them survive?
the last person yells out the first, second to last the second, etc. at least half survive?
Originally posted by: jersiq
Originally posted by: brikis98
To keep this thread going, I'll add one more, but I hope someone else has something for the future:
After losing a battle to his rival, an angry king decided that he would execute the 50 engineers he had in his employment. He marched them out on the field and prepared to execute them, but at the last second, the king felt pity and decided to give them one last chance to live.
The king explained to the engineers that on the following day, the 50 engineers would again be marched out onto a field. They would stand in a straight line, back to front, all facing the same direction, so each man sees just the backs of the men in front of him. The king's soldiers would then put, at random, either a red or black hat on each engineer. The engineer would be able to see all the hats of the men in front of him, but not his own or those of the men behind him.
The king would then start at the back of the line - that is, the engineer who can see the other 49 engineers in front of him - and ask: "is your hat red or black?" The engineer would then answer with one word: either "red" or "black". If he gets it right, he lives. If he gets it wrong, he is immediately executed. Either way, the king moves up the line asking the same question to each engineer in turn. If an engineer says anything other than "red" or "black" or if any of the engineers cheat (try to look at their own hats), all 50 are immediately executed.
Question: what strategy can the engineers come up with to guarantee the maximum number of them survive?
5 hats problem, not going to bother.
If you're bored, here's this:
prove that there are no whole number solutions for the following equation:
x^n+y^n=z^n {n|n>2}
Should keep you busy for a while.
Originally posted by: jersiq
Originally posted by: brikis98
To keep this thread going, I'll add one more, but I hope someone else has something for the future:
After losing a battle to his rival, an angry king decided that he would execute the 50 engineers he had in his employment. He marched them out on the field and prepared to execute them, but at the last second, the king felt pity and decided to give them one last chance to live.
The king explained to the engineers that on the following day, the 50 engineers would again be marched out onto a field. They would stand in a straight line, back to front, all facing the same direction, so each man sees just the backs of the men in front of him. The king's soldiers would then put, at random, either a red or black hat on each engineer. The engineer would be able to see all the hats of the men in front of him, but not his own or those of the men behind him.
The king would then start at the back of the line - that is, the engineer who can see the other 49 engineers in front of him - and ask: "is your hat red or black?" The engineer would then answer with one word: either "red" or "black". If he gets it right, he lives. If he gets it wrong, he is immediately executed. Either way, the king moves up the line asking the same question to each engineer in turn. If an engineer says anything other than "red" or "black" or if any of the engineers cheat (try to look at their own hats), all 50 are immediately executed.
Question: what strategy can the engineers come up with to guarantee the maximum number of them survive?
5 hats problem, not going to bother.
If you're bored, here's this:
prove that there are no whole number solutions for the following equation:
x^n+y^n=z^n {n|n>2}
Should keep you busy for a while.
Originally posted by: JS80
Originally posted by: brikis98
To keep this thread going, I'll add one more, but I hope someone else has something for the future:
After losing a battle to his rival, an angry king decided that he would execute the 50 engineers he had in his employment. He marched them out on the field and prepared to execute them, but at the last second, the king felt pity and decided to give them one last chance to live.
The king explained to the engineers that on the following day, the 50 engineers would again be marched out onto a field. They would stand in a straight line, back to front, all facing the same direction, so each man sees just the backs of the men in front of him. The king's soldiers would then put, at random, either a red or black hat on each engineer. The engineer would be able to see all the hats of the men in front of him, but not his own or those of the men behind him.
The king would then start at the back of the line - that is, the engineer who can see the other 49 engineers in front of him - and ask: "is your hat red or black?" The engineer would then answer with one word: either "red" or "black". If he gets it right, he lives. If he gets it wrong, he is immediately executed. Either way, the king moves up the line asking the same question to each engineer in turn. If an engineer says anything other than "red" or "black" or if any of the engineers cheat (try to look at their own hats), all 50 are immediately executed.
Question: what strategy can the engineers come up with to guarantee the maximum number of them survive?
the last person yells out the first, second to last the second, etc. at least half survive?
Originally posted by: brikis98
5 hats problem? What's that?
Oh, and your problem is Fermat's Last Theorem. I think I'll leave that one to the experts
Originally posted by: brikis98
I believe in MotionMan's answer, he means that N = 10, or whatever number was initially tails up...
Originally posted by: Aikouka
As for the other one, if you say... poke someone in the back if he's wearing red or don't if he's wearing black... does that constitute cheating?