1. ## A threesome

<img src=/w3timages/whiteline.gif width=33% height=2>

1) In my town, there is a hairdresser called Fred. Fred is the only hairdresser in my town, the other day he decided that he would shave all the town's people who do not shave themselves, but not the ones who do.

If Fred follows his rule, will he shave himself or not?

<img src=/w3timages/whiteline.gif width=33% height=2>

2) There are some palces on Earth wherethe following is true:

Starting from one of these points, you can walk 1 mile South, then 1 mile East, then 1 mile North, and you will end up back where you started.

One of these points is the North Pole. Can you tell me where the others are?

<img src=/w3timages/whiteline.gif width=33% height=2>

3) Four people are at a party and think of a number, they then each tell you something about it.

Albert: The number has 2 digits
Brian: The number is a divisor of 150
Christopher: The number is not 150
Dennis: The number is divisible by 25

One of these people is lying. Who is it?

<img src=/w3timages/whiteline.gif width=33% height=2>

Hint: Number 2 will need a mathematical proof

2. ## Re: A threesome

2) <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">All points of the circle around the south pole 1 mile north of the circle around the south pole with a circumference of 1 mile.
Also all points of the circle around the south pole 1 mile north of the circle around the south pole with a circumference of 1/2 mile, and 1/3 mile, etc.</span hide>

3. ## Re: A threesome

3. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Dennis is the liar.
For Numbers 1, 2, 3, 5 and 6 both Dennis and Albert would be liars.
For Number 150 both Albert and Christopher would be liars.
For 25, 50 and 75 all 4 would NOT be lying.
That leaves 10, 15, and 30 which are not divisible by 25 but do have 2 digits, are factors of 150 and <> 150
</span hide>

4. ## Re: A threesome

2)<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The south pole. I'm thinking along the lines of the prime meridian/equator...I just can't put the thought into the correct words... </span hide>

5. ## Re: A threesome

3) <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Dennis is lying.
If Albert were lying, Brian and Dennis speak the truth, so the number can only be 25, 50, 75 or 150, and since Christopher speaks the truth too, only 2-digit numbers remain possible - contradiction.
If Brian were lying, Albert and Dennis speak the truth, so the number can only be 25, 50 or 75, but those are all divisors of 150 - contradiction.
If Christopher were lying, Albert and Dennis speak the truth, so the number can only be 250, 50 or 75, so it is not 150 - contradiction.

Possible numbers are 15 and 30 - both have 2 digits, are divisors of 150, and are NOT divisible by 25.</span hide>

6. ## Re: A threesome

Well done Gary, have a [choccy bar]

7. ## Re: A threesome

1) <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Has he ever been shaved? He will not shave himself if he's already shaven.</span hide> <img src=/S/evilgrin.gif border=0 alt=evilgrin width=15 height=15>

8. ## Re: A threesome

Hans

I always feel I am entering the lions den when I am not happy with your answer <img src=/S/flee.gif border=0 alt=flee width=25 height=25>

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">You can not start 1 km away from the South Pole, if you did, you would not be able to do the second leg of the journey.</span hide>

9. ## Re: A threesome

1) <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">is a famous paradox. There is no solution.</span hide>

10. ## Re: A threesome

errr, Jeremy is that your answer, if so, <img src=/S/nope.gif border=0 alt=nope width=15 height=15>

12. ## Re: A threesome

1) <img src=/S/sarcasm.gif border=0 alt=sarcasm width=15 height=15><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">If a tree falls in the forest and nobody is around to hear it....</span hide>

13. ## Re: A threesome

1) Correct<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The answer to this one is that Fred cannot follow his own rule the way it is stated. If he shaves himself he is breaking it by shaving someone who shaves himself. If he doesn't - he breaks the rule by not shaving someone who doesn't shave himself.</span hide>

14. ## Re: A threesome

Hi Hans, have read it and still not happy... the answer does include<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">pi</span hide>

Maybe I have read it wrong but if you have a chance can you explain to me please?

15. ## Re: A threesome

I was too lazy to write out the nitty gritty details, but here goes. Strictly speaking, we'd have to do spherical geometry, but at the scale of the answer, we can pretend the earth is flat.
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Start at any point 1+1/(2*pi) miles away from (=north of) the south pole (brrr...)
Walk 1 mile south. You're now 1/(2*pi) miles away from the south pole.
Walk due east. You're following a circle around the south pole with radius 1/(2*pi), so its circumference is exactly 1 mile.
After one mile, you've come full circle. Walk 1 mile north to the starting point.

More general: start at any point 1+1/(n*2*pi) miles from the south pole, where n = 1, 2, 3, 4, ...
Walk 1 mile south. You're now 1/(n*2*pi) miles from the south pole.
Walk due east. You're following a circle around the south pole with radius 1/(n*2*pi), so its circumference is exactly 1/n mile.
After n full circles, you've walked 1 mile east. Walk 1 mile north to the starting point.</span hide>

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