Puzzle time

[markfiend]

1. A man stands in front of a painting of a man and tells us: "Brothers and sisters have I none, but this man's father is my father's son." Who is on the painting?
   a) His father
   b) He himself
   c) His son
2. It is dark in my bedroom and I want to get two socks of the same colour from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least one pair?
   a) 2
   b) 3
   c) 25
   d) 47
   e) 48
3. You are on an island called Texel, with inhabitants of the following types:
   Knights, who always tell the truth.
   Knaves, who never tell the truth.
   Normals, who sometimes tell the truth and sometimes lie.
   You meet one of the inhabitants and he tells you "I'm not a Knight". What type of inhabitant is he?
   a) Knight
   b) Knave
   c) Normal
   d) Indeterminable
4. A hunter leaves his cabin in the morning and walks one mile due south. Here he sees a bear and chases it for one mile due east before he shoots it. He then drags the bear one mile due north back to his cabin. What colour is the bear?
   a) Black
   b) Brown
   c) White
   d) Grey
5. A street contains 100 buildings numbered 1 to 100. How many nines are used in these numbers?
   a) 10
   b) 11
   c) 19
   d) 20
6. In a city, the following facts are true:
   No two inhabitants have the same number of hairs.
   No inhabitant has exactly 40360 hairs.
   There are more inhabitants than there are hairs on the head of any one inhabitant.
   What is the largest possible number of inhabitants?
   a) 0
   b) 40359
   c) 40360
   d) 40361
7. Consider two cans, the first contains one litre of milk and the second one litre of water. Take one cup of milk out of the first can and pour it into the second can. After mixing, (assuming the mixture to be even throughout the can) take one cup of the mixture from the second can and pour it back into the first can. Which of the following statements is true?
   a) There is more water in the first can than milk in the second can.
   b) There is less water in the first can than milk in the second can.
   c) There is as much water in the first can as there is milk in the second can.
   d) None of the above statements is true.
8. Alice meets the Lion and the Unicorn in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. The Unicorn lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. They make the following statements to Alice:
   Lion: "Yesterday was one of my lying days."
   Unicorn: "Yesterday was one of my lying days too."
   What day is it?
9. A Cretan named Epimenides once said to a fellow Cretan: "All Cretans are liars". Assuming that a liar always lies and someone who is not a liar always tells the truth, which of the following statements is true?
   a) Epimenides is a liar.
   b) Epimenides is not a liar.
   c) It is indeterminable whether Epimenides is a liar or not.
10. Recall Texel and its inhabitants: Knights (who always tell the truth), Knaves (who always lie) and Normals (who sometimes lie and sometimes tell the truth). A man and a woman may only marry if they are both Normal, or if one of them is a Knight and the other a Knave. Mr and Mrs A tell you the following:
    Mr A: "My wife is not Normal"
    Mrs A: "My husband is not Normal"
    What types of person are Mr and Mrs A?
    a) They are both Normal.
    b) Mr A is a Knight and Mrs A is a Knave.
    c) Mr A is a Knave and Mrs A is a Knight.
    d) indeterminable

[emilystrange]

mark, it's MONDAY.

[markfiend]

[culprit]

so much for my quiet relaxing lunchbreak!!

[Ed Rhombus]

Noted my answers down.

Can we have the answers?

[markfiend]

Give the nocturnal types a chance. I'll post the answers tomorrow.

I could PM you the answers now actually. Give me a mo to type them up.

[andymackem]

I'll have forgotten my answers before you post them up tomorrow.

And after the event nobody would believe it if I got any of them right.

[canon docre]

I'll have forgotten my answers before you post them up tomorrow.

And after the event nobody would believe it if I got any of them right.

If you're so eager to show-off, why don't you pm your answers to Markfiend? He can publicise your glory later on.

[markfiend]

I'll do a PM of the answers to you too Andy.

[Ed Rhombus]

Nice one

[markfiend]

Some smart-arse has prompted me to make the following addition to question 7:

(assuming the mixture to be even throughout the can)

[lazarus corporation]

Some smart-arse has prompted me to make the following addition to question 7:

(assuming the mixture to be even throughout the can)

damn smartarses who introduce additional factors, such as the specific gravity of milk

[boudicca]

1. A man stands in front of a painting of a man and tells us: "Brothers and sisters have I none, but this man's father is my father's son." Who is on the painting?
   a) His father
   b) He himself
   c) His son

b) He himself

[*]It is dark in my bedroom and I want to get two socks of the same colour from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least one pair?
a) 2
b) 3
c) 25
d) 47
e) 48

b) 3 - But put the light on, stupid!

[*]You are on an island called Texel, with inhabitants of the following types:
Knights, who always tell the truth.
Knaves, who never tell the truth.
Normals, who sometimes tell the truth and sometimes lie.
You meet one of the inhabitants and he tells you "I'm not a Knight". What type of inhabitant is he?
a) Knight
b) Knave
c) Normal
d) Indeterminable

c) Normal

[*]A hunter leaves his cabin in the morning and walks one mile due south. Here he sees a bear and chases it for one mile due east before he shoots it. He then drags the bear one mile due north back to his cabin. What colour is the bear?
a) Black
b) Brown
c) White
d) Grey

f**k right off!!!

[*][*]A street contains 100 buildings numbered 1 to 100. How many nines are used in these numbers?
a) 10
b) 11
c) 19
d) 20

d) 20

[*]In a city, the following facts are true:
No two inhabitants have the same number of hairs.
No inhabitant has exactly 40360 hairs.
There are more inhabitants than there are hairs on the head of any one inhabitant.
What is the largest possible number of inhabitants?
a) 0
b) 40359
c) 40360
d) 40361

d) 40361

[*]Consider two cans, the first contains one litre of milk and the second one litre of water. Take one cup of milk out of the first can and pour it into the second can. After mixing, (assuming the mixture to be even throughout the can) take one cup of the mixture from the second can and pour it back into the first can. Which of the following statements is true?
a) There is more water in the first can than milk in the second can.
b) There is less water in the first can than milk in the second can.
c) There is as much water in the first can as there is milk in the second can.
d) None of the above statements is true.

d) None of the above statements is true.?... dunno I'm thinking about alcohol right now TBPH...

[*]Alice meets the Lion and the Unicorn in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. The Unicorn lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. They make the following statements to Alice:
Lion: "Yesterday was one of my lying days."
Unicorn: "Yesterday was one of my lying days too."
What day is it?

Thursday?

[*]A Cretan named Epimenides once said to a fellow Cretan: "All Cretans are liars". Assuming that a liar always lies and someone who is not a liar always tells the truth, which of the following statements is true?
a) Epimenides is a liar.
b) Epimenides is not a liar.
c) It is indeterminable whether Epimenides is a liar or not.

I'm really running out of steam now, plumping for C, which is probably incorrect...

[*]Recall Texel and its inhabitants: Knights (who always tell the truth), Knaves (who always lie) and Normals (who sometimes lie and sometimes tell the truth). A man and a woman may only marry if they are both Normal, or if one of them is a Knight and the other a Knave. Mr and Mrs A tell you the following:
Mr A: "My wife is not Normal"
Mrs A: "My husband is not Normal"
What types of person are Mr and Mrs A?
a) They are both Normal.
b) Mr A is a Knight and Mrs A is a Knave.
c) Mr A is a Knave and Mrs A is a Knight.
d) indeterminable[/list]

Ach I'm sick of this...

[markfiend]

5/10

And I'm not telling you which five because then people won't bother to get the answers themselves.

[boudicca]

5/10

And I'm not telling you which five because then people won't bother to get the answers themselves.

Oh dear.

[lazarus corporation]

This one's my favourite (and I got it right - using logic not guesswork ):

A hunter leaves his cabin in the morning and walks one mile due south. Here he sees a bear and chases it for one mile due east before he shoots it. He then drags the bear one mile due north back to his cabin. What colour is the bear?
a) Black
b) Brown
c) White
d) Grey

[boudicca]

Now I know the answers, they all seem so simple!

Don't you hate it when that happens!!!

[paint it black]

This one's my favourite (and I got it right - using logic not guesswork ):

A hunter leaves his cabin in the morning and walks one mile due south. Here he sees a bear and chases it for one mile due east before he shoots it. He then drags the bear one mile due north back to his cabin. What colour is the bear?
a) Black
b) Brown
c) White
d) Grey

white

[paint it black]

I'm really running out of steam now, plumping for C, which is probably incorrect...

he is a cretan, and therefore any all statement must be inclusive

[lazarus corporation]

well, I got 8/10 (or arguably 9/10 - I'll leave MF to decide whether my 'specific gravity of milk' argument gets me the extra point )

[James Blast]

is the answer to all of them Naomi Campbell?

[timsinister]

is the answer to all of them Naomi Campbell?

It should be.

[markfiend]

ANSWERS

1. c His son.
   "My father's son" must be himself as he has no siblings. So he is telling us that he is the subject's father.
2. b three socks.
   After taking two out, you either already have a pair or one of each colour. If you don't have a pair, the third sock out must match one of them.
3. c Normal.
   A Knight always tells the truth and therefore could never deny being a Knight.
   A Knave always lies, and for him to say "I'm not a Knight" would be true.
   A Normal sometimes lies and sometimes tells the truth, so there is no contradiction in him telling the truth this time.
4. c White.
   The only place in the world where it is possible to travel one mile south, one mile east, then one mile north and end back where you started is the North Pole. The bear must be a polar bear.
5. d 20
   9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
   Count them!
6. c 40360
   If we number the inhabitants by the number of hairs they possess (as no two inhabitants have the same number) they will be 0, 1, 2, 3, 4...
   If there can be no inhabitant number 40360 (no inhabitant has exactly 40360 hairs) this is where the numbering must stop; there must be more inhabitants than hairs on the hairiest individual which is no longer possible after a gap.
   0, 1, 2, 3... 40358, 40359 is a total of 40360 inhabitants.
   (I've not made this explanation very clear I'm afraid.)
7. c There is as much water in the first can as milk in the second.
   let c be the volume of a cup.
   After taking a cup of milk from can 1 to can 2 we have:
   Can 1 contains (1-c) litres of milk
   Can 2 contains 1 litre of water and c litres of milk.
   After mixing, the cup removed from can 2 contains:
   water and milk in the proportions 1:c, with a total volume c
   So: c/(1+c) water and (c^2)/(1+c) milk
   This is added back to can 1:
   Can 1 now contains (1-c) + (c^2)/(1+c) milk and c/(1+c) water
   Can 2 now contains 1 - c/(1+c) water and c - (c^2)/(1+c) milk
   As (1-c) + (c^2)/(1+c) = 1 - c/(1+c) we can see that there is as much water in the first can as milk in the second.
8. Thursday.
   Both animals say "Yesterday was one of my lying days".
   Therefore for both animals, either he is telling the truth (so it was a lying day yesterday and a truth day today) or he is lying (so it is a lying day today and was a truth day yesterday)
   The only day when it is possible for this to be the case for both animals is Thursday.
9. a. Epimenides is a liar.
   It is impossible that Epimenides is telling the truth, for if all Cretans are in fact liars then so is Epimenides.
   It is also impossible for no Cretans to be liars, as Epimenides is a Cretan.
   Therefore it must be the case that some Cretans are not liars, and some Cretans (Epimenides among them) are liars.
10. a They are both Normal.
    If Mr and Mrs A are Knight and Knave (in either combination) it would be impossible for the one who is a Knave to truthfully state that their spouse, a Knight, is not Normal. Therefore they must both be Normal (who sometimes lie and sometimes tell the truth).

[markfiend]

well, I got 8/10 (or arguably 9/10 - I'll leave MF to decide whether my 'specific gravity of milk' argument gets me the extra point )

No. It was just an after-the-fact rationalisation of a wrong answer!

[timsinister]

Congratulations Herr Moderator, you've conclusively proved that the average Heartlander's logical deduction skills have completely failed!