Ark's Perplexing Puzzles

[arkvoodle]

That's what I thought at first, but how does the second person communicate to the third the color of the third's hat when he can only say the color of his own?

You can save about 50% by having everyone guess randomly.

You can save 50% or more if every even person agrees to call out the color of the hat in front of them. That way the person in front knows what color their hat is, and if the person behind also has the same colored hat then both will survive.

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.

1) Bertie is the mole (he would be the only one lying in this instance)

2) If there were two moles... It would be Cedric and Albert, because Bertie would be the only one telling the truth.

Correct!

Bertie is the mole. Both Albert and Cedric are telling the truth. Hence, when Albert said, "Bertie is a mole," he was telling the truth, and giving you the correct answer. When Bertie said, "Cedric is a mole," he was lying, as he himself is a lying mole. When Cedric responded, "Bertie is lying," he was telling the truth, and also affirming that Bertie was lying.

In the second case, if there were 2 moles, the identifications would be a direct inverse. Both Albert and Cedric would be moles, and Bertie would be telling the truth.

12PP for you.

Puzzle 019- Crossing the River- 15PP

A man needs to cross a river in a canoe. With him, he has a bag of grain, a chicken, and a fox. He can only carry one of the three at a time. If he leaves the grain and the chicken, the chicken will eat the grain. If he takes the grain, the fox will eat the chicken.

How does he successfully cross the river with his load?

 

[Locke]

eh, I had edited my post before that so as not to double-post, but I don't have any way of proving that so I guess I lost that one. Thanks for the explanation on the hats though.

 

[dur.i.am]

You can save about 50% by having everyone guess randomly.

You can save 50% or more if every even person agrees to call out the color of the hat in front of them. That way the person in front knows what color their hat is, and if the person behind also has the same colored hat then both will survive.

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.



Correct!

Bertie is the mole. Both Albert and Cedric are telling the truth. Hence, when Albert said, "Bertie is a mole," he was telling the truth, and giving you the correct answer. When Bertie said, "Cedric is a mole," he was lying, as he himself is a lying mole. When Cedric responded, "Bertie is lying," he was telling the truth, and also affirming that Bertie was lying.

In the second case, if there were 2 moles, the identifications would be a direct inverse. Both Albert and Cedric would be moles, and Bertie would be telling the truth.

12PP for you.

Puzzle 019- Crossing the River- 15PP

A man needs to cross a river in a canoe. With him, he has a bag of grain, a chicken, and a fox. He can only carry one of the three at a time. If he leaves the grain and the chicken, the chicken will eat the grain. If he takes the grain, the fox will eat the chicken.

How does he successfully cross the river with his load?

Takes the Chicken over, comes back for the Grain.
Takes the Grain over, comes back with the Chicken.
Takes the Fox over, comes back for the Chicken.
Tales the Chicken over.

 

[arkvoodle]

Takes the Chicken over, comes back for the Grain.
Takes the Grain over, comes back with the Chicken.
Takes the Fox over, comes back for the Chicken.
Tales the Chicken over.

Perfect! 15PP for you sir.

Puzzle 020- Marital Ages- 10PP

If you add the age of a man to the age of his wife, the result is 91. He is now twice as old as she was when he was as old as she is now.

How old is the man and his wife?

 

[dur.i.am]

Perfect! 15PP for you sir.

Puzzle 020- Marital Ages- 10PP

If you add the age of a man to the age of his wife, the result is 91. He is now twice as old as she was when he was as old as she is now.

How old is the man and his wife?

54 and 27

 

[Locke]

he's 52, she's 39. 52+39=91.
When he was 39, she was 26. 52 is twice 26.


using four variables, x1=man's younger age, x2=man's older age, y1=woman's younger age, y2=woman's older age,
we're given four equations:
x2+y2=91
x2=2*y1
x1=y2
x2-x1=y2-y1
solve.

That was a fun one!

 

[arkvoodle]

he's 52, she's 39. 52+39=91.
When he was 39, she was 26. 52 is twice 26.


using four variables, x1=man's younger age, x2=man's older age, y1=woman's younger age, y2=woman's older age,
we're given four equations:
x2+y2=91
x2=2*y1
x1=y2
x2-x1=y2-y1
solve.

That was a fun one!

Correct 7PP for you.

Puzzle 021-Marbles -10PP

Given twelve marbles that are identical in size, shape, and color, determine which single marble is heavier in weight than the others. You are supplied with a balance and must conclude your determination in three weighings.

 

[Locke]

one: weigh four marbles against four marbles
if the scales are even:
two: weigh the other four agaisnt each other, 2v2
three: switch two. If the scale switches, the marble you just put on the heavier side is the heaviest. If the scale does not switch, it's the one you left on the heavier side.

if one side is heavier:
two: take off two from each side
if one side is still heavier:
three: switch two. (same as step three above)
if they're even
three: weigh the two that you took off the heavier side against each other.


EDIT(11/1 12:43 AM):
there's a slightly simpler way that yields the same result but is easier to explain:
one: weigh 4v4. Two things could happen:
A - the scales are even. In this case, you'd get rid of all the marbles on the scale and
two: weigh the remaining four 2v2, then remove the ones on the ligher side and
three: weigh the remaining two 1v1.
B - the scales are uneven. In this case, you'd get rid of the four marbles you didn't weigh and the four on the lighter side and follow steps two and three above.

 

[zants follower]

you did this already but it was with coins... I think

 

[Locke]

you did this already but it was with coins... I think

You're right; #2. Except you didn't know whether the fake coin was heavier or lighter, so the most efficient method yielded a worst case of 4 weighings. If we already know the odd one out is heavier than the rest, you can use a slightly different method (detailed above) with a worst case of 3. There might be a better way of doing the coins to get a worst case of 3, but there's no reason for me to think about it.

 

[athenian200]

Ark's Perplexing Puzzles- Number 001- Brain Food- 15 PP

You have three boxes of fruit.
One contains just apples, one contains just oranges, and one contains a mixture of both.

Each box is labeled -- one says "apples," one says "oranges," and one says "apples and oranges."

However, it is known that none of the boxes are labeled correctly.

How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?

Apples and Oranges = Box A
Apples = Box B
Oranges = Box C

All labels are false.

Well, Box A CAN'T be apples and oranges, because it has to be wrong. So whatever fruit you pull out of that, has to be either all oranges, or all apples. So you can label that one correctly.

If you pulled an apple out of box A, that means Box B must contain Oranges, and that Box C must contain both fruits, in order for all to be false.

If you pulled an orange out of box A, that means Box B must contain both fruits, and that box C must contain apples, in order for all to be false.

Does that work?

EDIT: ACK! Never mind, I didn't look at the rest of the thread before posting. Sorry. Just disregard this post.

 

[arkvoodle]

one: weigh four marbles against four marbles
if the scales are even:
two: weigh the other four agaisnt each other, 2v2
three: switch two. If the scale switches, the marble you just put on the heavier side is the heaviest. If the scale does not switch, it's the one you left on the heavier side.

if one side is heavier:
two: take off two from each side
if one side is still heavier:
three: switch two. (same as step three above)
if they're even
three: weigh the two that you took off the heavier side against each other.


EDIT(11/1 12:43 AM):
there's a slightly simpler way that yields the same result but is easier to explain:
one: weigh 4v4. Two things could happen:
A - the scales are even. In this case, you'd get rid of all the marbles on the scale and
two: weigh the remaining four 2v2, then remove the ones on the ligher side and
three: weigh the remaining two 1v1.
B - the scales are uneven. In this case, you'd get rid of the four marbles you didn't weigh and the four on the lighter side and follow steps two and three above.

CoRrEcT~! 10PP to you.

And @Athenian, i've accidentally replied to the first post by accident on a few occasions. Don't worry about it.

Next Puzzle comin' up!

Puzzle 023- Statements of Fact? -5PP

A. The number of false statements here is one.

B. The number of false statements here is two.

C. The number of false statements here is three.

D. The number of false statements here is four.


Which of the above statements is true?

 

[Josh]

E. None of the Above.

 

[arkvoodle]

E. None of the Above.

Incorrect Sir Josh.

 

[athenian200]

Puzzle 023- Statements of Fact? -5PP

A. The number of false statements here is one.

B. The number of false statements here is two.

C. The number of false statements here is three.

D. The number of false statements here is four.

I think that it's C, three. Because if any one of the statements are true, all of the others are false. Which means three are false and one is true. And presumably, at least one must be true because in order to choose an answer, you must be picking a true statement.

D contradicts itself by implying that all the statements are false, but if it's true, then not all the statements are false, thus making IT false. A and B imply that more than one statement can be true at one time, which makes no sense because they conflict with each other.