

He was also the face of Guinness in the UK for many years  despite being allergic to it!
Another of the Good Guys is gone ... (But not , just in case)
Sent from my Amstrad PC 1640
Never throw anything away, Griff
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
AntiTwitter: @DalekDave is now a follower!





Just saw that on Faceslap, another legend has left the building.
R.I.P.
Technician
1. A person that fixes stuff you can't.
2. One who does precision guesswork based on unreliable data provided by those of questionable knowledge.
JaxCoder.com





Oh man, another one? at 75!





I just saw this earlier. Well, that sucks. RIP, Rutger.






I still reckon one of his best/most realistic/natural/believable characterization was in Hitcher.
it's one of the few movies that actually upset me.





I agree, but I was even more upset that someone in Hollywood felt the need to remake it recently.





agree the remake was a stupid idea, wasn't that old, (wasn't a huge hit either), why???
... didn't watch it, never will  the Hauer version was too damn good perfect





He lived just down the road from me. We'd bump into each other, when he was over here.
The movies made him look a lot younger and fitter than he was. He suffered quite badly, in the past few years.
I wanna be a eunuchs developer! Pass me a bread knife!





He was born in Breukelen, the Netherlands, just a few km's away from my house.
Trivia  Brooklyn (NY) was originally called Breukelen.





Not all pasta goes to parties – some of it's cannelloni.
Sent from my Amstrad PC 1640
Never throw anything away, Griff
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
AntiTwitter: @DalekDave is now a follower!





Orzo they say.
"the debugger doesn't tell me anything because this code compiles just fine"  random QA comment
"Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers."  chriselst
"I don't drink any more... then again, I don't drink any less."  Mike Mullikins uncle





maybe a BYO party? couldn't afford it, no money, not a penne
Message Signature
(Click to edit >)





These Italian jokes are getting rotini.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
 6079 Smith W.





and some describe small acne problem...Ziti!
Technician
1. A person that fixes stuff you can't.
2. One who does precision guesswork based on unreliable data provided by those of questionable knowledge.
JaxCoder.com





And some is macaronri
(Language warning)
Socialism is the Axe Body Spray of political ideologies: It never does what it claims to do, but people too young to know better keep buying it anyway. (Glenn Reynolds)





... when you look up and you realize you're the only one in your group who's in the office today. Everybody else on vacation except for one guy, and he's working from home.
I hear the barbarians at the gates.
It's been nice knowing youuuuuuuuuuuuuuuuuuuuuuuuuCARRIER LOST
Software Zen: delete this;





Gary Wheeler wrote: I hear the barbarians at the gates. Then be careful what you say.[^]
I have lived with several Zen masters  all of them were cats.
His last invention was an evil Lasagna. It didn't kill anyone, and it actually tasted pretty good.





Quote: Only the lonely (dumdumbdummy doowah)
Know the way I feel tonight (ooh yay, yay, yay, yeah)
Only the lonely (dumdumbdummy doowah)
Know this feeling ain't right (dumdumbdummy doowah) Lyrics~Only The LonelyRoy Orbison  YouTube[^]





I'm reminded of the shortest science fiction story ever told, which was based upon the following lines from Thomas Bailey Aldrich[^]:The last man on Earth sat alone in a room.
There was a knock at the door...
Software Zen: delete this;





Here is a very well written Open Source Discrete Math book:
Discrete Mathematics  An Open Introduction[^]
You can download the PDF for free.
Interactive Book(Read it online)
Even if you're not interested in the book, check out how nicely the interactive book is done.
Discrete Mathematics  interactive book[^]
About The Book: The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proofs" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.
Four main topics are covered: counting, sequences, logic, and graph theory. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions helps students gain familiarity with the language of mathematics, and two additional topics (generating functions and number theory) are also included.
Here's a nice puzzle example (you've probably seen before)
Quote: While walking through a fictional forest, you encounter three trolls guarding a bridge. Each is either a knight, who always tells the truth, or a knave, who always lies. The trolls will not let you pass until you correctly identify each as either a knight or a knave. Each troll makes a single statement:
Troll 1: If I am a knave, then there are exactly two knights here.
Troll 2: Troll 1 is lying.
Troll 3: Either we are all knaves or at least one of us is a knight.
Which troll is which?





OK, time to embarrass myself horribly:
raddevus wrote: Troll 3: Either we are all knaves or at least one of us is a knight.
That statement cannot possibly be false. Therefore, Troll 3 is a knight.
raddevus wrote: Troll 2: Troll 1 is lying.
If that were true, then Troll 1 would be a knave, and Troll 2 would be a knight. But that would mean that Troll 1's statement was true.
Therefore, Troll 2 is a knave. Which means that Troll 1 is not lying, making him a knight.
The fact that there are exactly two knights doesn't affect the truth of Troll 1's statement, since it was a logical implication, which only applies in one direction. If the lefthand side is false, then the statement is true regardless of the state of the righthand side.
On a related note, there's a simple solution to this drinking game: Saturday Morning Breakfast Cereal  Drink[^]
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
 Homer





I'm very glad that you took a shot at it and felt uncertain about the answer, because I feel the same way.
Unfortunately, I didn't find the answer in the book.
Here's my logic though.
I thought Troll 2 was the only possibility for a knight.
I thought he was telling the truth that Troll 1 (a knave) was lying.
Troll 3 has to be lying because if all 3 were knaves, they'd all be lying and since Troll 1 and Troll 2 are in conflict with each other, one of them has to be telling the truth.
But, I cannot exactly rectify part 2 of Troll 3's statement (at least one of us is a knight).
But, I am entirely unsure about everything.
Is your answer correct? I will look it over again and see if it all seems to reconcile.
Thanks again for putting yourself out there. Maybe someone will come along who is confident of the answer.
Reposting riddle for reference:
Quote: While walking through a fictional forest, you encounter three trolls guarding a bridge. Each is either a knight, who always tells the truth, or a knave, who always lies. The trolls will not let you pass until you correctly identify each as either a knight or a knave. Each troll makes a single statement:
Troll 1: If I am a knave, then there are exactly two knights here.
Troll 2: Troll 1 is lying.
Troll 3: Either we are all knaves or at least one of us is a knight.
Which troll is which?
Edit
Solution 2 from me
as I read it again, I think that Troll 1 and Troll 3 are knights.
I think Troll 2 is lying that Troll 1 is lying so Troll 1 is a knight.
"My intellect is quite dizzying!!! Wait til I get started!!" ala Princess Bride. Princess Bride  "Truly, you have a dizzying intellect."  YouTube[^]
Then Troll 3 could be telling the truth that "at least one of us is a knight" (since there are two knights.
So
Troll 1 Knight
Troll 2 Knave
Troll 3 Knight
I've probably embarrassed myself more.
modified 24Jul19 17:21pm.





raddevus wrote: Troll 3: Either we are all knaves or at least one of us is a knight.
There's literally no way that statement could be a lie.
(Unless the setup of the riddle was a lie, and they're not all either knights or knaves. But that would be too devious.)
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
 Homer



