Two players are playing a game of dice. Player A rolls two dice, then takes away the die with
the lowest score. Now Player B rolls a single die. If he can beat Player A's score, he wins;
he also wins if he equals Player A's score.
1. What is Player B's chance of winning?
2. The rules are changed so that Player A has to reroll any 6s he gets until he gets a lower
number. What are Player B's chances of winning now?
3. The rules are changed again, so that player A is allowed to roll 6s, but whenever B rolls a 1
he can roll again until he gets a better number. What is Player B's chance of winning now?
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That's a little complex, but not too bad. But I'm still trying to figure
out if you bought any of that junk I threw at you on the Boy/Girl thing.
I love to agitate on this stuff. And it's amazing what some people will
believe. I doubt you're one of them, though. You have your math
together, like I try to do with my grammar...and sometimes with my
grampa, too.
I know the answer, but I'm not sure I can type that much explanation
without typer's cramp, so I'll see what others say.
Coyote
LOL... I feel like such a fool. Why did I reply to a post that had the line "70% of children are
born male"? It's a tendency of mine to respond to something as if it were serious, even when
it is probably a joke. Well it's good to hear you haven't joined the Dark Side; the Force
needs more people like you, Coyote!
As for maths, the key to it all is logical thought, which is an incredible tool to have at your
disposal: if you could master it completely (which I doubt any human being could) it would
give you the intellectual equivalent of an infinitely sharp knife, which you could use to
puncture any argument that is logically unsound, and a supply of unbreakable material, which
you could use to form a scaffold of logic that will withstand all attacks. However, even
someone far, far below this level (such as myself) can produce something that is extremely
resistant to casually thrown bricks, and any kind of knife is sharper than bare fists.
If I find a better way of saying that last paragraph, I might put it in my profile. I don't know
why I posted that problem, I just like puzzles, which is one reason why I'm studying Maths.
Hint: a 6-sided die where all 6s have to be rerolled is exactly equivalent to a 5-sided die.
You have a good point regarding logic, but it can only go so far, right?
I heard a story of a philosophy professor somewhere down south
(Virginia if I recall correctly) who logically proved that one of his
students was a cheeseburger to win a bet. My point is that you can
prove anything to be true, as long as you have a stronger knowledge
of logic than your opponent; it doesn't necessarily matter whether your
premises are true in reality...
OK, I'm not going to go any further, I don't want to get into a
discussion of ultimate truth or anything like that!
Joe
There is an excellent book called "Straight and Crooked Thinking"
which describes the use of logic in debates and highlights ways in
which people can make you think you are a cheeseburger, for
example, but more importantly, how you can recognise when it's
happening. Essential reading for any politician, I'd reckon...
How to attack a logically sound argument: dig into its foundations (ie the assumptions on
which it is based) and wedge in some explosives. You might not destroy the argument, but
you will make it fall over, which is usually good enough (unless you happen to be in a
philosophy class :-) .)
If you dare not attack the foundations (eg if they are also supporting your arguments), try
declaring the argument irrelevant and walking around it.
(For example, on the boy/girl thing, my answer would be based on assumptions like babies
only come in two sexes, that each is equally common, and that the sex of one child has no
bearing on the sex of the other, all of which could be easily blown up!)
However, you can't prove just anything to be true; what about the statement "This statement
is false.", the logical equivalent of the perpetual-motion cat?
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You're being quite kind! Thanks. I DID push the limits puposely with
70%. I thought of making it 55%, but I wanted you to get where I was
going. Maybe...here's a thought: I should just say what I mean, or
identify my humor as such. Then you would know, and not tend to feel
foolish. My fault. Someday, I'll actually be logical and mathmatically
advanced enough not to go on the long skids I do on this chess site.
Well, maybe that's going a bit too far. To the Force! Or any other type
of checkmate you can devise.
Coyote
I too have done one thing on RHP as a joke, but not labelled it as such (see my post on
Calm). This also resulted in people getting the wrong end of the stick. When we use a web
forum, we are all socially handicapped, because we cannot see the body language of the other
person; for this reason I very rarely react emotionally to what is said. So my post was more
trying to say "This person is wrong, and ought to be corrected" than "What an idiot!"
As for the "Dark Side", I am referring to those who think Dinotopia is realistic (it was
apparently very popular in the US, but if you've seen it, you'll know what I mean) and those
who think science is a religion (hence Acolyte - another joke) or worse, an evil conspiracy.
That kind of attitude really does scare me, and seems to be on the rise at the moment.
Hence my serious response to your non-serious post. No need to label your humour as such -
it just made me laugh even more when I realised what you had done!
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That's cool! Just always remember that the one body language
characteristic I always retain when writing is a sparkle in my left eye.
As for Dinotopia: I saw it, and it's reeeeealy dumb. But it was kinda'
fun, anyway.
Science...a religion? Well, it definitely isn't, and God has certainly used
many brilliant scientists to care for all people. The sad thing is that
many have made science a religion the same way they have done with
God. My stand is that God is active in science and hates religion with
the exception of true religious actions: Caring for the poor, visiting
prisoners, healing the infirm (no matter what that looks like), forgiving
one another, restoring the downtrodden, etc. That is religion true and
undefiled and it is definitely no joke! (It also is where the sparkle
comes from.)
Coyote
Hey, and if 70% of children were actually born male, girls (who
become women, of course) would no longer find it necessary to attract
men. No need to look pretty, smell nice, be clean and be soft to
touch. ...Hmmm, almost sounds like they would be like guys!
Oooooo, what a terrible thought... 🙂