ElspethInnle
1. 6 x (6 x (2 x 2)) = 144
2.
3. Aim so that Garth's opponent ends up with 9, or 5, or 1. As Garth gets to start, he can pick 2, to get a total of 9 branches still in play.
For each turn after that, he needs to make sure that both his and his opponents goes add up to 4 (If his opponent takes 3 sticks, Garth takes one, leaving the numbers
5 or 1, ensuring the opponent is always stuck with the last branch).
4. 9 years, double the amount of bugs will not affect the rate at which the taint is eaten. If you simply double 1 bug at the beginning, it will still take 9 years because you're not doubliing the amount of bugs each year, just the first year.
5. Elspeth - 2
Domick - 1
Rushton - 5
Dameon - 10
Domick and Elspeth cross with the torch (2 minutes)
Domick returns with the torch (1 minute)
Rushton and Dameon cross with torch (10 minutes)
Elspeth returns with torch (2 minutes)
Domick and Elspeth cross with torch (2 minutes)
(Total of 17 minutes)
6. Tallest = 1, second tallest = 2, second shortest = 3 and shortest = 4
Depending on the amount of white/black hat ratio:
3 white/black v 1 black/white:
1 can see, if the three hats in front of them are all the white, they have the black hat. If they see two whites, and one black, they can be sure that they have the remaining white hat.
If number 2 can see two of the same coloured hats in front of them, after hearing 1's verdict, they can decided whether they have the remaining white hat or the black one.
Number 3 will be able to guess the colour of their hat from what 1 & 2 say, and what they can see of 4. 4 must make a guess based on what the other three say.
If there are 2 black and 2 white,
1 will be able to see if there are 2 whites in front of them, they must have the remaining black.
The other's would be able to make educated guesses based on what the previous person says.
As long as they each say their guess in turn.
sezzaxox
1. 48, unless of course the misfit is Dameon and then he doesn't see any of them.
2. They should place the balls in the shape of a five pointed star, with a ball at each point, and then at the base of each point
3. 3
4. 6.6 years
5. Elspeth and Dom cross first taking 2minutes
Dom returns 1 minute
Rushton and his pig and Dameon cross 10 minutes
Elspeth returns taking 2 minutes
Elspeth and Dom cross again taking 2 minutes
6. If the tallest sees 3 black hats they should announce White, if they see 3 white hats they should announce black, if they see 2 black or white and 1 white or black they should remain quite. The second tallest should announce white if they see two black hats or black if they see two white hats, if they wee one of each they should remain quite. The third tallest should say the black if they see one white hat, or white if they see one black hat. The shortest should say whichever colour the previous hatted person didn't say. It should keep 3 of them alive at the least
Morgan le Fay
1. 6 rebels, 6 stable hands, 12 horses, 24 children: 36 people and 12 animals
2. The five lines are arranged in the form of a pentagram, which is a pentagonal star. Five carved balls have to be placed on each of the five peaks of the star and on each of the five places, where two lines cross each other.
3. Garth has to remove two branches. If the rebel then takes one branch, Garth takes three, if the rebel takes two branches, Garth takes two and if the rebel takes three branches, Garth takes one. however, after Garth removed branches twice, there still have to be five branches left. Now, if the rebel takes one branch, Garth takes three, if the rebel takes two branches, Garth takes two, if the rebel takes three branches, Garth takes one. In any way, there will be one branch left for the rebel to remove. He is bound to lose this way.
4. The bugs will have finished eating up the tainted stuff of the grounds in nine years if Garth has twice as many insects to start with.
5. First, Elspeth and Domick have to cross the bridge. That will take them 2min. Domick returns with the torch to the others which takes him 1min. He passes on the torch to Rushton and Dameon who need 10min to cross. They hand the torch over to Elspeth waiting who goes back to get Domick which takes 2min. Elspeth and Domick cross as well and after 2 more min, everybody's on the other side.
2+1+10+2+2= 17
6. One misfit (the tallest) might die, but not more:
Plan: If the tallest one can see two same colours and one which is different, he calls out the colour which he only sees once.
The second tallest can then conclude from the two colours in front of him what his own colour is (two same colours -> he has the colour the tallest said; two different colours -> he has the other colour, not the one the tallest said).
Then the thrid tallest knows his colour as well (if the second had the colour the tallest said -> he will have the other colour; if the second didn't have the colour the tallest said and the one if front of him hasn't either -> the third has the colour the tallest said; if the second didn't have the colour the tallest said, but the one in front of him has -> the third has the same colour the second had).
From that the third knows his colour as well (won't repeat it all now, you should get my point, as you made the riddle ;-) )
But there is another possibility:
The tallest might see three colours which are the same. In this case he should just shut up. After a little while, the other three people know that the tallest is silent because they all have the same colours on their heads.
The second tallest then knows his colour, because it is the same colour the two people in front of him wear and the second knows as well because the smallest one wears the same colour.
The smallest one knows as soon as the second and the third misfit have voiced their colours.
In any case: The tallest has a 50:50 chance of survival. In the first case, he calls out the colour that is only represented once yet, so there is the chance, that his colour of the hat might be his own as well. In the second case he doesn't say anything to begin with. But his chances might be higher if he guesses the colour that the other three misfits don't wear.
Let's keep our fingers crossed all of them make it >.<
Fay
deb
Deb of the Mystics
Brain Teaser.
1. 258
2.
3. 2
4. 2.5 years
5. Domick and Elf cross first, Domick returns and Rushton and Dameon go. Elspeth returns then Domick and Elspeth cross again. Though reasonably, Dameon does not need the torch so Elspeth could cross back while Dameon is still crossing, after Rushton has crossed saving a bit more time.
6. Depending if the hats were of equal number, two black,, two white. All would survive if the tallest person could see all the hats and know that the odd one would be the one he wore.
Benno
Q1. 186 people, 72 animals, 256 altogether
Q2.-
Q3. 2 sticks must be picked up.
Q4. 2 and a half years
Q5.-
Q6. 3 people can be saved by the tallest person calling out the name of the person in front of them, and so on.
Bibliophile
1.
158(plus the other members of their own group)
2.
3.
Garth must pick two the first round, then on the other rounds pick so that the number he chooses when added to the number the other person has chosen equals 4 (eg 2,[ 3, 1],[ 2, 2], 1)
4.
5 years
5.
Elspeth and Dommick across - 2min
Domick back - 2+1=3min
Rushdon and Dameon across 3+10=13min
Elspeth back - 13+2=15min
Domick and Elspeth across - 15+2=17min
6.
Three possible solutions:
- Arrange beforehand that the tallest person will call out the colour of the shortest person’s hat (or similar combination). The tallest person has a 50/50 chance of surviving; the shortest person can then call out the correct colour and all others survive.
- Or, work out a code beforehand that lets one person tell the person in front of them the colour of their hat by tapping them (or similar). All survive.
- Or, given that they are Misfits...
Arrange for one person to farseek another and tell them the correct colour. All survive
Fate
Hi Moonfairies! Here are my answers to the Brain Teaser challenge. It's like playing a Professor Layton game all over again... :P
[ligne][/ligne]
1. 6 + 36 + 72 + 148 = 262
2. See Image:
3. Two sticks
4. 9 years
5. (Domick) & (Elf) Cross with Torch = 2 mins
(Domick) Returns with Torch = 1 mins
(Rushton) & (Dames) Cross with Torch = 10 mins
(Elf) Returns with Torch = 2 mins
(Domick) & (Elf) Cross with Torch = 2 mins
Total = 17 mins
6. All can be saved except the tallest Misfit, as he has no way to figure out whether his own hat is black or white. However the Misfits can formulate a plan so that all the others can be saved. First, the tallest Misfit has to say aloud "black" if there are an even number of black hats in front of him, or "white" if otherwise. Then the second tallest Misfit can figure out his own hat colour, and then all the others can figure their own out and say it out loud.
Livia
The answers to the Brain Teaser Questions are:
1. The misfits see a total of 258 people and animals
2. The wooden balls must be placed in the shape of a five point star so that the lines which shape the star have four balls per line. I've drawn an image in paint (which is not very good so sorry for my lack of talent! :P ) which might help to better describe how the balls are positioned.
The black star is the basic shape, the brown balls show where they are to be positioned and the red lines show that there are 5 lines, each of which have 4 balls in them.
3. Garth must initially remove 2 balls so that 9 of the 11 remain. He must then make sure that for every two turns, that a total of 4 sticks are removed (ie. if his opponent takes 1, Garth takes 3. If his opponent takes 2 then so does Garth, if his opponent takes 3 then Garth takes one) This way the amount of sticks is as follows:
Garth removes 2 sticks to begin the game. This leaves 9.
In the next two turns, the opponent remove x amount of stick and Garth removes y amount, where x + y = 4. This leaves 5 sticks.
Same thing for the next two turns, the opponent removes 1 or 2 or 3 sticks and Garth removes 3 or 2 or 1 correspondingly, to ensure that only 1 stick is left and it is the opponents turn.
I hope this makes sense, I know I haven't explained it very well so sorry for that! :P
4. If there are twice as many bugs to begin with, it will take 9 years to clear the tainted lands. (I think.. :P )
5. Ok, so the order in which the misfits cross the bridge is.. Elspeth & Domick cross first, taking 2mins, Dom comes back taking 1 minute. Then Dameon & Rushton cross next slowly, taking 10 minutes. Next Elspeth crosses back, taking 2 minutes, then finally Dom and Elspeth return to the other side, taking 2 minutes. This takes a total of 17 minutes. Again, I've drawn a little something to help explain the crossing, apologies for the poor artistry.. :P
6. The only way I can think of solving this puzzle, since there is no garantee of how many of each colour hat there will be is that the Misfits decide, before they begin is that the tallest of them will call out the opposite colour to that of the misfit directly in front of them. There is a 50/50 chance that they will be right or wrong. The 2nd tallest misfit then calls out the opposite colour to that which the first misfit called out, knowing that the first misfit could see what colour hat they were wearing and called out the other instead. The 3rd misfit, being only able to see the shortest in front of them, calls out the opposite colour of the hat in front and the shortest misfit calls out the opposite colour of the hat colour just announced. So, by signalling the 2nd and 4th misfits, their lives can always be spared and the 1st and 3rd misfits have a 50%chance of surviving. Hope this makes sense. As long as the misfits work out a system where the 1st and 3rd reveal to the 2nd and 4th what their colours are then the 2nd & 4th can definitely survive and the 1st and 3rd have a 50/50 chance of surviving. (this one was rather hard and I feel like I've gotten it wrong as I don't want anyone to die! :P )
Hope all this makes sense! Many thanks to your hard working moonfairies! ;)
ariadne
1. 258
2. Place them in a star shape
3. 1
4. twice as fast
5. 1st: Elspeth and Domick. Domick goes back across.
2nd: Rushton and the Pig cross. Elspeth goes back.
3rd Domick and Dameon cross. Domick goes back.
4th Domick and Elspeth cross.
(This is my best guess, and the time in no way works :( Oh, and I assumed the pig was counted in all that :-/ )
6. I have no idea :P
Cheers
kieran
Ashlings Guild
1. 258 people/animals
2. http://i1088.photobucket.com/albums/i327/Kieranthony/Brainteaser2.jpg
3. Garth should first take 2 first, then take the number of branches that will allow (opponent + Garth) = 4 in each successive round. Thus 2+4+4=10, opponent must take 11th.
4. Tainted ground cleared in 9 years.
5. Dom, El, Rush, Dam. Domick goes first, with Elspeth, and Elspeth holds the torch. When Domick gets across after 1 minute, Elspeth waits for Rushton. Rushton will take 3 minutes to reach Elspeth at the middle, then Rushton takes the torch, stops, and Elspeth continues across. By the time Elspeth is across, five minutes will have past, and Dameon gets on. Dameon reaches Rushton at the middle after five minutes more. Dameon takes the torch and they both continue, Rushton will take only 3 more minutes, and Dameon reaches the end after they have been after a total 15 minutes for everyone.
6. The tallest person guesses whatever colour they observe to be least common. Say this is black. Regardless of whether their guess is right or not, the three people in front know that either two of them have white (the colour that the tallest observed to be most common) and 1 black or all have white. If the next person sees black on one of the 2 ahead, then they can guess white and must be right, if not then they still guess black (and have a 50:50 chance) to indicate that the other two definitely have white. Having said black, then if they die the two in front are safe, and if they live the three of them are safe. If they guess white because a black is still ahead, then the shortest two know that one of them has black and one has white; therefore, the second shortest will be right so long as they guess the opposite colour to the one they see ahead, thus indicating to the shortest what not to pick. So 0.5 probability of losing the tallest (0.5x0.5=0.25) probability of losing the next, but the tallest two can ensure that shortest two survive.
Sian
1.
186 humans and 72 horses
2.
3.
Garth must remove three branches, leaving 8 remaining. His opponent may reduce this to 7, 6 or 5, but whatever number he reduces it by, Garth can then reduce that number to four. Then it doesn't matter how many branches his opponent takes, there will be more than 0, but less than four, meaning that Garth can then reduce the total to zero.
4.
The tainted lands will be cleared in 9 years. This is an exponential problem with a base of 2, where the index represents the total number of years minus one. Doubling the initial conditions adds one to the index, so this only makes a difference of one year.
5.
It doesn’t particularly matter whether Elspeth or Rushton goes first, but Rushton is unwilling to leave his betrothed alone in the dark with Dameon, so Elspeth and Domick must cross together first. This takes 2 minutes.
Domick carries the torch back across the bridge to Rushton, this takes 1 minute.
Domick and Rushton cross the bridge. This takes 5 minutes.
Domick walks back across the bridge to tell Dameon he can cross. 1 minute.
Domick begins the walk first, carrying the torch and takes 1 minute.
Thus far, 10 minutes have elapsed and Domick, Rushton and Elspeth are on the other side. Seven minutes after this, Maik’s man returns and Dameon is still crossing, but that doesn’t matter because he’s blind and doesn’t need a torch => the guard won’t be able to see him. Two minutes after that, Dameon reaches the other side and the group travels onwards.
6.
Three of the misfits can be saved. The fourth has a fifty-fifty chance of survival. When each misfit shouts out which colour hat they are wearing, the tallest goes first and uses a code to tell the person in front what colour hat that person is wearing. For example; “I am wearing a _______ coloured hat!†indicates that the person in front’s hat is white while “I think I’ve got a _____ coloured hat on!†indicates that the person in front’s hat is black. The second tallest person goes next, followed by the second shortest, followed by the shortest. In this way they can tell each other what coloured hat the person in front of them is wearing.
Each participant can only shout out a guess to the colour of the hat they are wearing. If they get it wrong then they are killed.
