Signpost puzzles

[Kieran Child]

I used to make tonnes of these. I'll post two here:

You arrive at a town and find a notice on the town noticeboard from the town's mayor
It reads
"Oh god oh god oh god. You'll never guess what's happened. A plague has hit our town and it lingers in the air, infecting people like a good'n. We have cleared a single pathway from here to the town hall. Also, to help you find the way, I hired some of the townspeople to put up signs . Unfortunately, the plague has turned a couple of them mad, so while some townspeople tell the truth, some of them lie. That's what plague does to you, yasee."

The first signpost has

NW: Keep away! Plague!
W: More than 1 of these signs is false
SW: Keep away! Plague!

You then travel to the second signpost which has

N: Keep away! Plague!
NE: If you go this way you'll meet the same fate as had you gone north
E: You came from this direction, jerkass
SE: Keep away! Plague!
S: There are more than 4 false statements here
SW: If you go south-east, nothing bad will happen to you
W: True statements and false statements alternate
NW: True statements and false statements don't alternate

Feel free to answer, but try making your own. They're darned fun.

[Phil Reynolds]

Feel free to answer

OK, well assuming that the (unstated) question is "What is the safe route to the town hall?" then there seem to be multiple answers for the second junction. The first one is easy enough: go west (young man). Otherwise, one of the statements associated with the other directions is false, which means that the sign pointing west causes an inevitable contradiction: if it's true, it's false, and vice versa.

When we come to the second junction, one possible answer could be: go north-east. The truth table for the various statements then becomes:

N: Keep away! Plague! - true
NE: If you go this way you'll meet the same fate as had you gone north - false
E: You came from this direction, jerkass - true
SE: Keep away! Plague! - true
S: There are more than 4 false statements here - false
SW: If you go south-east, nothing bad will happen to you - false
W: True statements and false statements alternate - false
NW: True statements and false statements don't alternate - true

However, an equally valid answer could be to go south-east, which produces the following truth table instead:

N: Keep away! Plague! - true
NE: If you go this way you'll meet the same fate as had you gone north - true
E: You came from this direction, jerkass - true
SE: Keep away! Plague! - false
S: There are more than 4 false statements here - false
SW: If you go south-east, nothing bad will happen to you - false
W: True statements and false statements alternate - false
NW: True statements and false statements don't alternate - true

In fact, I think the only way you know you can't go (apart from doubling back on yourself) is north.

[Kieran Child]

In that second truth table, you've said something bad will happen to you by going south east, and then went there anyway.

[Phil Reynolds]

In that second truth table, you've said something bad will happen to you by going south east, and then went there anyway.

Sorry, yes, that line should have read:

SW: If you go south-east, nothing bad will happen to you - true

My original working was right - the error crept in when I copied-and-pasted the table for the case where the answer is NE and edited it for the answer being SE. My point still remains: either of these is a valid answer (as are S, SW, W and NW) on the basis of the information given.

[Kieran Child]

oooh you make a good point.
This is a corrected version:
N: Keep away! Plague!
NE: If you go this way you'll meet the same fate as had you gone north
E: You came from this direction, jerkass
SE: Keep away! Plague!
S: There are 3 false statements here
SW: If you go south-east, nothing bad will happen to you
W: True statements and false statements alternate
NW: True statements and false statements don't alternate

must be someone else on here who makes puzzles who could make another signpost?

[Phil Reynolds]

oooh you make a good point.
This is a corrected version:

OK, so there is still no single right answer. I haven't bothered this time trying it for all directions, but the truth tables involve no contradictions if either N or NE is assumed to be the right answer.

[Kieran Child]

gah I'm going to need to work on that one. The intended answer is NE.... hmm....