There was once a recluse who never left his home. The only time anyone ever visited him was when his food and supplies were delivered, but they never came inside. Then, one storm winter night when an icy gale was blowing, he had a nervous breakdown. He went upstairs, turned off all the lights and went to bed. Next morning, he had caused the deaths of several hundred people. How?
There was once a recluse who never left his home. The only time anyone ever visited him was when his food and supplies were delivered, but they never came inside. Then, one storm winter night when an icy gale was blowing, he had a nervous breakdown. He went upstairs, turned off all the lights and went to bed. Next morning, he had caused the deaths of several hundred people. How?
You are asked to clean out your neighbour's basement. It is quite large and there are 3 lightbulbs to cover the whole basement. However your neighbour is a miser and will only let you turn on one at a time. There are 3 light switches outside the basement and there is no way of telling which one turns on which bulb without going into the basement. You figure out a way to determine which switch turns on which bulb by only going down the stairs once without coming back up. How?
A woman gave natural birth to two sons who were born on the same hour of the same day of the same month of the same year. But they were not twins and she had no access to a time machine. How could this be?
A woman gave natural birth to two sons who were born on the same hour of the same day of the same month of the same year. But they were not twins and she had no access to a time machine. How could this be?
A stark raving mad king tells his 100 wisest men he is about to line them up and that he will place either a red or blue hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat.
The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.
The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.
The king will then move on to the next wise man and repeat the question.
The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.
What is the maximum number of men they can be guaranteed to save?
Then use next switch and run into room. If light is on you know it is the second switch.
If light is off but the bulb is warm it is the first switch.
If off and cold it is third one
Well done
Clue for the dog one - the fact that the house is 20m away from the kennel and the rope is only 10m long isn't important, the house could be 11m away or 50m and the riddle would still work.
A stark raving mad king tells his 100 wisest men he is about to line them up and that he will place either a red or blue hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat.
The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.
The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.
The king will then move on to the next wise man and repeat the question.
The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.
What is the maximum number of men they can be guaranteed to save?
The wise men can save 99 if each man gives the colour of the hat in front of him as his own colour, and the person in front knows this. The unlucky first person to go cannot guarantee his own safety. It is probable that the king knows this and will alternate the first two hats, though, so something can be worked out between the first two men by which the first man will give the opposite colour to the one the second man has, with the second one knowing this.
I thought that but surely number two will be correct, but number three won't know as the number two has said his colour not the colour of the one in front?
You're on the right lines but still out for the hat one. Bear in the mind the riddle is 'how many can definitely be saved' and it is probably higher than you reckon.
If you see more blue than red hats in front of you, say Blue
If you see more red than blue hats, say Red
If equal, stick with what the previous person said
If there are the same number of red as blue, saying, for instance, Blue will result in you being killed, but if the next person sees that the numbers of hats are now equal they can presume that they have a blue hat and stick with Blue. If the next person sees that the number of red hats is more they can say Red - if they have a blue hat they are expendable - sorry - but then the next person will either see a majority of reds (in which case they know they have a blue hat) or an equality (in which case they know they have a red hat) - at which point my entire schematic breaks down
If you see more blue than red hats in front of you, say Blue
If you see more red than blue hats, say Red
If equal, stick with what the previous person said
If there are the same number of red as blue (EVEN), saying, for instance, Blue will result in you being killed, but if the next person (ODD) sees that the numbers of hats are now equal they can presume that they have a blue hat and stick with Blue. If the next person (EVEN) sees that the number of red hats is more they can say Red - if they have a blue hat they are expendable - sorry - but then the next person (ODD) will either see a majority of reds (in which case they know they have a blue hat) or an equality (in which case they know they have a red hat) - at which point my entire schematic breaks down
Uhhh lemme think a bit more
Wait - if there's been one swap from everyone saying Blue to everyone saying Red, then everyone in front will know that if the latter person reverts to saying Blue then they are simply self-preserving. And so the NEXT (EVEN) person knows that the previous person was right. And because they are even, they will see an odd number of hats, so one must prevail - if they see more red then they know their own hat is blue and vice versa. Everyone subsequent to this can use this logic to save themselves - the men simply agree to say which one is more prevalent UNTIL one of them says something different, after which everyone will be able to work it out.
If there are 97 blues and 3 reds, then no matter where the reds are, almost all will be saved simply by giving the majority.
If there are 45 blues and 55 reds, then no matter where the blues are, at least 55 will be saved (if all the blues come first - if they're more scattered, more will probably be saved).
If there are 50 apiece, then if all the Blues precede all the Reds, then all the Reds will be saved.
Answer is 99. So how can 99 people be saved? The first wise man counts all the red hats he can see (Q) and then answers "blue" if the number is odd or "red" if the number is even. Each subsequent wise man keeps track of the number of red hats known to have been saved from behind (X), and counts the number of red hats in front (Y).
If Q was even, and if X&Y are either both even or are both odd, then the wise man would answer blue. Otherwise the wise man would answer red.
If Q was odd, and if X&Y are either both even or are both odd, then the wise man would answer red. Otherwise the wise man would answer blue.
At the recent BrainBashers Festival, the 100 metres heats were closely monitored.
Each contestant had to run in two races so that the average place could be determined.
Only one runner finished in the same place in both races.
Alan was never last. Charles always beat Darren. Brian had at least one first place. Alan finished third in at least one of the races. Both Darren and Charles had a second place.
Comments
Then use next switch and run into room.
If light is on you know it is the second switch.
If light is off but the bulb is warm it is the first switch.
If off and cold it is third one
2 boys and a girl?
The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.
The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.
The king will then move on to the next wise man and repeat the question.
The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.
What is the maximum number of men they can be guaranteed to save?
Clue for the dog one - the fact that the house is 20m away from the kennel and the rope is only 10m long isn't important, the house could be 11m away or 50m and the riddle would still work.
Another clue - this isn't a maths riddle
This is in fact a maths problem.
If you see more blue than red hats in front of you, say Blue
If you see more red than blue hats, say Red
The dog one - the rope isn't tethered at the other end
You're on the right lines but still out for the hat one. Bear in the mind the riddle is 'how many can definitely be saved' and it is probably higher than you reckon.
If you see more red than blue hats, say Red
If equal, stick with what the previous person said
If there are the same number of red as blue, saying, for instance, Blue will result in you being killed, but if the next person sees that the numbers of hats are now equal they can presume that they have a blue hat and stick with Blue. If the next person sees that the number of red hats is more they can say Red - if they have a blue hat they are expendable - sorry - but then the next person will either see a majority of reds (in which case they know they have a blue hat) or an equality (in which case they know they have a red hat) - at which point my entire schematic breaks down
Uhhh lemme think a bit more
If there are 97 blues and 3 reds, then no matter where the reds are, almost all will be saved simply by giving the majority.
If there are 45 blues and 55 reds, then no matter where the blues are, at least 55 will be saved (if all the blues come first - if they're more scattered, more will probably be saved).
If there are 50 apiece, then if all the Blues precede all the Reds, then all the Reds will be saved.
All other scenarios permit more survival.
My answer is 50.
Answer is 99. So how can 99 people be saved? The first wise man counts all the red hats he can see (Q) and then answers "blue" if the number is odd or "red" if the number is even. Each subsequent wise man keeps track of the number of red hats known to have been saved from behind (X), and counts the number of red hats in front (Y).
If Q was even, and if X&Y are either both even or are both odd, then the wise man would answer blue. Otherwise the wise man would answer red.
If Q was odd, and if X&Y are either both even or are both odd, then the wise man would answer red. Otherwise the wise man would answer blue.
Each contestant had to run in two races so that the average place could be determined.
Only one runner finished in the same place in both races.
Alan was never last. Charles always beat Darren. Brian had at least one first place. Alan finished third in at least one of the races. Both Darren and Charles had a second place.
What were the two results?