| QUOTE (veg @ Feb 1 2004, 09:36 AM) |
7.The pitcher, catcher, and infielders except Allen, Harry, and Andy, are shorter than Sam.
This is a biggie...First this makes Sam an outfielder so strike him from all infield, pitcher and catcher positions. Then strike out Allen, Harry, and Andy from all the outfield positions. |
I assumed that Allen Harry and Andy HAD to be infielders. (and all the infielders except..) I mean it doesn't make sense if say harry is the pitcher and then say, "the pitcher except for harry".
| QUOTE |
10.Sam is involved in a divorce suit. The catcher and the third baseman each have two children. Ed, Paul, Jerry, the right fielder, and the center fielder are bachelors. The others are married.
Makes Sam Married. Catcher and third base also married. Also makes the only position Sam can hold as Left field because right and center are Bachelors. Eliminate Sam from all positions other then left field. Eliminate Ed, Paul, Jerry from center and right field. Eliminate Ed, Paul, Jerry from any known Married position - Third, catcher, pitcher.
|
This is another thing I saw. I don't like to assume things in riddles (i assumed the above because of how it ws written) but I did not think that the were all married with children. So after the first time I tried it witht hem married and still messed up.
I like your method of drawing all the positions, I just did an old school graph. Thanks for the explaination.
Yeah that's the problem with these kind of riddles.
The way the sentences are structured will mess you up. And you have to make assumptions. Sometimes you assume wrong and it dorks up your answer.
I always thought the pitcher and the catcher were concidered infielders but in this case they separate them from the other infielders.
I tried putting everthing into a table but I kept getting lost so I came up with the chart idea.
bill - center fielder
mike - right fielder
sam - left fielder
ed - shortstop
andy - third baseman
jerry - second baseman
paul - first baseman
allen - catcher
harry - pitcher
| QUOTE (p027867 @ Feb 2 2004, 04:43 PM) |
| What is more powerful than god, more evil than the devil, the rich want it, the poor have it and if you eat it, you will die? |
| QUOTE (p027867 @ Feb 2 2004, 09:43 PM) |
| What is more powerful than god, more evil than the devil, the rich want it, the poor have it and if you eat it, you will die? |
Nothing
The Answer: The Butler did it!! Page 36 is on the
back of page 35 so the butler couldn't have put the
bill between the two pages.
Dang...I guess that riddle was too easy. Congrats to veg for being the first to solve the riddle and Krill123 for being the second. Anyway, here's another one. I wouldn't really call this a riddle, but hope you know the Bible. Good luck!!!
EPISODE X
There are 16 books of the Bible in the following paragraph...can you find them?
I once made a remark about the hidden books of the Bible. It was a lulu; kept people looking so hard for facts and for others it was a revelation. Some were in a jam especially since the names of the books were not capitalized, but the truth finally struck home to
numbers of readers. To others, it was a real job. We want it to be a most fascinating few moments for you. Yes there will be some really easy ones to spot. Others may require judges to help them. I will quickly admit it usually takes a minister to find one of them, and there will be loud lamentations when it is found. A little lady says she brews a cup of tea so she can concentrate better. See how well you can compete. Relax now for there really are sixteen names of the books in the Bible in this story
Have fun!!!
note: this took too long to do
For those who did not see the 16 books of the Bible, here they are:
I once made a remark about the hidden books of the Bible. It was a lulu; kept people looking so hard for facts and for others it was a revelation. Some were in a jam especially since the names of the books were not capitalized, but the truth finally struck home to numbers of readers. To others, it was a real job. We want it to be a most fascinating few moments for you. Yes there will be some really easy ones to spot. Others may require judges to help them. I will quickly admit it usually takes a minister to find one of them, and there will be loud lamentations when it is found. A little lady says she brews a cup of tea so she can concentrate better. See how well you can compete. Relax now for there really are sixteen names of the books in the Bible in this story.
-----------------------------
Okay, so far I've posted 10 riddles. The riddles started with a few sentences to becoming a whole paragraph. Some where easy and some where...hard? Now, the riddles will become harder to solve. I want to stomp someone. Hopefully I could do that. I had people thinking in Episode VIII. Are you guys ready? Here we go...
EPISODE XI
A legendary king possessed a huge amount of gold. He hid this treasure carefully: in a building consisting of a number of rooms. In each room there were a number of boxes; this number was equal to the number of rooms in the building. Each box contained a number of golden coins that equaled the number of boxes per room. When the king died, one box was given to the royal barber. The remainder of the coins had to be divided fairly between his six sons.
Is a fair division possible in all situations? Good Luck!!!
yes, a fair division in all situations is possibe, each son will get nothing
Cleary, that's right. Can you explain how you got your answer?
)
- the royal barber was givin one box with "s" coins
- the 6 brothers, S³ - "s" coins remain
with all this done you get this problem: S(S - 1)(S + 1).
- the last part is divisible by 6, if a number is divisible by 6, it is also divided by 3 and even. ( which this problem is )
- so we got "s" whatever it is. the problem is: S(S - 1)(S + 1), and this always has 3 successive numbers. in this problem one of them is always divisible by 3, and another one is always even.
- so this is S=1 ( which doesn't give the boys jack shit
)
thats how i did it. i was gonna scan the sheet of paper i did it on, but my scanner is broken.
ok
| QUOTE |
ok, so we got a number of rooms. we'll call this "s"
- each room has "s" boxes - each box has "s" coins
so this also equals: SxSxS=S³ ( "x" represents times )
- the royal barber was givin one box with "s" coins - the 6 brothers, S³ - "s" coins remain
with all this done you get this problem: S(S - 1)(S + 1). - the last part is divisible by 6, if a number is divisible by 6, it is also divided by 3 and even. ( which this problem is )
- so we got "s" whatever it is. the problem is: S(S - 1)(S + 1), and this always has 3 successive numbers. in this problem one of them is always divisible by 3, and another one is always even.
- so this is S=1 ( which doesn't give the boys jack shit ) |
hmm...this answer seems remarkably similar to this one
Solution to: King Midasand if you did work it out all on your own, you still got the answer partially wrong. yes, fair division is always possible, but the only case where this...
| QUOTE |
| each son will get nothing |
is true, is if S=1. any other number will result in the sons receiving some amount of gold equally.
tsk tsk tsk
| CODE |
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|
GETTER DONE!!! Well, here's another one! This one may be very easy. Good Luck!!!
EPISODE XIIThere is a scientific method to determining what these words have in common. Can you figure it out?
GAGE, HOER, NO, LACE, OF, SIPS, ARK

[EDIT] Hehe, I misspelled a few elements.
[/EDIT]
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|
Did you enjoy the image? Anyway, here's another one. Good Luck!
EPISODE XIII
Triangle numbers are formed by adding successive integers, i.e.
1 = 1+0,
3 = 1+2,
6 = 1+2+3,
10 = 1+2+3+4,
etc.
So the first few triangle numbers would be:
1,3,6,10,15,21,28, ...
Suppose somebody tells you a random integer. How can you quickly find out whether or not it is a triangle number?
why do I feel like I'm back in my old highschool algebra class?
This is exactly my FST class ( Funstions Statistics Trigonometry)
Ok,
n! Which is the same as n C k
k!(n-k)!
Where n is the row number and k is the position in that row, counting from top to bottom and from left to right. Also, we start counting from zero, so the 6 above would be in the row 4 and column 2.
The rows of Pascal's triangle also represent coefficients of a binomial raised to a power. Consider:
(a+b )4
If we expand this, we get:
a4+4a3b+6a2b2+4ab3+b4
The coefficients are the 4th row of Pascal's triangle:
1 4 6 4 1
O wait i did not really answer your question
Yeah, kinda like:
Multiply the number by 8 then add 1. If the result is a perfect square, then the original number is a triangle number.
For example: 10*8+1 = 81. 81 = 9^2. So 10 is a triangle number.
11*8+1 = 89. 89 is not a perfect square, so 11 is not a triangle number.
Okay, I don't think that was really a riddle. But here's one:
EPISODE XIV
The king dies and two men, the true heir and an impostor, both claim to be his long-lost son. Both fit the description of the rightful heir: about the right age, height, coloring and general appearance.
Finally, one of the elders proposes a test to identify the true heir. One man agrees to the test while the other flatly re-fuses. The one who agreed is immediately sent on his way, and the one who re-fused is correctly identified as the rightful heir.
Can you figure out why? Good Luck!!!
uh... I give up. I've been thinking about it for too long and haven't gotten a good answer yet.
| QUOTE (NooberTehGod @ Feb 11 2004, 01:43 AM) |
| he asks for a blood test or something like that. The king's son was a hemopheliac, or whatever, and therefor would never submit to being cut for fear of dying of blood loss |
yup
Damn those are hard... only got one right i think... any more?
| QUOTE (katsumoto @ Feb 11 2004, 12:14 PM) |
| what position in line gives him the greatest chance of being the first duplicate birthday? |
in front of the line, he won't get the free ticket but he has a better chance to be the first duplicate birthday.
and for that last one.... I thought about a blood test but I figured the one guy wouldn't do it since it would show he isn't the king's son. Whatever.. keep them coming.
Yea thats what i was thinking too.
15-25th person in line.
actually 2nd in line.. it doesn't hurt his chances of being the first duplicate and if by some wierd chance the guy in front of him is the same.. he gets a free ticket.
Here's why:
Suppose he was the Kth person in line. Then he wins if and only if the K-1 people ahead all have distinct birtdays AND his birthday matches one of theirs. Let
A = Fred's birthday matches one of the K-1 people ahead
B = those K-1 people all have different birthdays
Then
Prob(Fred wins) = Prob(B ) * Prob(A | B )
(Prob(A | B ) is the conditional probability of A given that B occurred.)
Now let P(K) be the probability that the K-th person in line wins, Q(K) the probability that the first K people all have distinct birthdays (which occurs exactly when none of them wins). Then
P(1) + P(2) + ... + P(K-1) + P(K) = 1 - Q(K)
P(1) + P(2) + ... + P(K-1) = 1 - Q(K-1)
P(K) = Q(K-1) - Q(K) <--- this is what we want to maximize.
Now if the first K-1 all have distinct birthdays, then assuming uniform distribution of birthdays among D days of the year, the K-th person has K-1 chances out of D to match, and D-K+1 chances not to match (which would produce K distinct birthdays). So
Q(K) = Q(K-1)*(D-K+1)/D = Q(K-1) - Q(K-1)*(K-1)/D
Q(K-1) - Q(K) = Q(K-1)*(K-1)/D = Q(K)*(K-1)/(D-K+1)
Now we want to maximize P(K), which means we need the greatest K such that P(K) - P(K-1) > 0. (Actually, as just given, this only guarantees a local maximum, but in fact if we investigate a bit farther we'll find that P(K) has only one maximum.) For convenience in calculation let's set K = I + 1. Then
Q(I-1) - Q(I) = Q(I)*(I-1)/(D-I+1)
Q(I) - Q(I+1) = Q(I)*I/D
P(K) - P(K-1) = P(I+1) - P(I)
= (Q(I) - Q(I+1)) - (Q(K-2) - Q(K-1))
= Q(I)*(I/D - (I-1)/(D-I+1))
To find out where this is last positive (and next goes negative), solve
x/D - (x-1)/(D-x+1) = 0
Multiply by D*(D+1-x) both sides:
(D+1-x)*x - D*(x-1) = 0
Dx + x - x^2 - Dx + D = 0
x^2 - x - D = 0
x = (1 +/- sqrt(1 - 4*(-D)))/2 ... take the positive square root
= 0.5 + sqrt(D + 0.25)
Setting D=365 (finally deciding how many days in a year!),
desired I = x = 0.5 + sqrt(365.25) = 19.612 (approx).
The last integer I for which the new probability is greater then the old is therefore I=19, and so K = I+1 = 20.
...viola!
EPISODE XVI
Land of the giants, it is often called,
Where warriors and wizards play with wolves;
Its suns and stars get hot and cold,
Whether one is at home or on the road.
Fourteen tribes live in the west, we are told,
One less than those in the eastern world;
The weakest thirteen will give up and fold.
While the strongest continue their quest for gold.
The kings are powerful and the magic is bold,
Others can fly and are a site to behold;
But when the season is past and the story is told,
New stars are born and old tribes evolve.
What is the Land of the Giants?
Have fun witht his riddle. Good Luck!!!
| QUOTE (katsumoto @ Feb 12 2004, 12:02 PM) |
Well...clblanch1622 solved the problem. Fred should try to be the 20th person in line. Congrats.
Here's why:
Suppose he was the Kth person in line. Then he wins if and only if the K-1 people ahead all have distinct birtdays AND his birthday matches one of theirs. Let A = Fred's birthday matches one of the K-1 people ahead B = those K-1 people all have different birthdays Then Prob(Fred wins) = Prob(B ) * Prob(A | B )
(Prob(A | B ) is the conditional probability of A given that B occurred.)
Now let P(K) be the probability that the K-th person in line wins, Q(K) the probability that the first K people all have distinct birthdays (which occurs exactly when none of them wins). Then
P(1) + P(2) + ... + P(K-1) + P(K) = 1 - Q(K) P(1) + P(2) + ... + P(K-1) = 1 - Q(K-1)
P(K) = Q(K-1) - Q(K) <--- this is what we want to maximize.
Now if the first K-1 all have distinct birthdays, then assuming uniform distribution of birthdays among D days of the year, the K-th person has K-1 chances out of D to match, and D-K+1 chances not to match (which would produce K distinct birthdays). So Q(K) = Q(K-1)*(D-K+1)/D = Q(K-1) - Q(K-1)*(K-1)/D Q(K-1) - Q(K) = Q(K-1)*(K-1)/D = Q(K)*(K-1)/(D-K+1)
Now we want to maximize P(K), which means we need the greatest K such that P(K) - P(K-1) > 0. (Actually, as just given, this only guarantees a local maximum, but in fact if we investigate a bit farther we'll find that P(K) has only one maximum.) For convenience in calculation let's set K = I + 1. Then Q(I-1) - Q(I) = Q(I)*(I-1)/(D-I+1) Q(I) - Q(I+1) = Q(I)*I/D
P(K) - P(K-1) = P(I+1) - P(I) = (Q(I) - Q(I+1)) - (Q(K-2) - Q(K-1)) = Q(I)*(I/D - (I-1)/(D-I+1))
To find out where this is last positive (and next goes negative), solve x/D - (x-1)/(D-x+1) = 0
Multiply by D*(D+1-x) both sides: (D+1-x)*x - D*(x-1) = 0 Dx + x - x^2 - Dx + D = 0 x^2 - x - D = 0
x = (1 +/- sqrt(1 - 4*(-D)))/2 ... take the positive square root = 0.5 + sqrt(D + 0.25)
Setting D=365 (finally deciding how many days in a year!), desired I = x = 0.5 + sqrt(365.25) = 19.612 (approx).
The last integer I for which the new probability is greater then the old is therefore I=19, and so K = I+1 = 20.
...viola! |
| QUOTE (katsumoto @ Feb 19 2004, 03:56 PM) |
| How old is the PRIEST?? |
36

just so you know, i didnt cheat or know the answer prior, i figured it mathematically
once you figure out what Fifty and Ten Dozens Twenty is your good
HINT: Read the riddle very carefully!
31?
63...
or possibly something to do with their is only one stranger that is 3 years old? But couldn't figure from here
PRIEST?
Would that be you, or me?
What do a Rubix cube and a penis have in common?
You have been zapped into this room by means unknown. There are two doors on one side of the room, there are two computers. It even seems they are each guarding a door.
There are two signs, and a leper in the room with you.
The first sign reads:
"Behind one door is God realization. Behind the other door is a room painted entirely green. The only things in that room are a man and a ladder, both of which are painted entirely green. The man has been hired by the coalition of Gangsta Rappers to hurl a non-stop barrage of insults at anyone who enters the room. " (end sign 1)
The second sign sits between the two computers (also the two doors) and reads as follows:
"One of these computers is programmed to lie to you regardless of how friendly you are to the user interface, the other computer is programmed to tell the truth, regardless of your emotional state."
It is about this time that the gangrenous leper begins to speak "I get you deal on phone time $.08 minutes weekdays all odd hours. $.10 on Thursday except the hour between 2:00 and 3:00, or any registered birthday . . . "
He begins to - quite slowly - lurch towards you, he's already reaching out towards you, you get the sense he's a "touchy-feely" sorta person. You quickly calculate you have time to ask one computer one question before he reaches you. The riddle before you is this: What question do you ask, and to which computer do you pose your question? Remember, you don't know whether the computer's answer will be a lie, and you've got to figure out which door to go out.
Hints:
1) You've heard great things about God realization, 2) It doesn't matter which computer you ask, i.e. there's an answer for both.
Ask what the other computer would say and go the opposite way.
Time for my math riddle.
What is the Xbox RSA key used to sign XBE files?
Go!
| QUOTE (Moleman @ Feb 27 2004, 10:16 PM) |
| What is the Xbox RSA key used to sign XBE files? |
42
| QUOTE (lordvader129 @ Feb 28 2004, 12:35 AM) |
| QUOTE (Moleman @ Feb 27 2004, 10:16 PM) | | What is the Xbox RSA key used to sign XBE files? |
42
|
That's just the answer to life, the universe, and everything. But what's the question?
MS signs all XBEs with "42" to make them run on an stock xbox
(wouldnt it be sick if that was true? lol)
EPISODE XIX
To the bold, I am a weapon;
To the gallant, I am a pin;
To the gracious, I am a service;
To the bridesmaid, I am a win.
To the traitor, I am a bribe;
To the star, I am a screen;
To the swift, I am an arrow;
To the bride, I am a dream.
What am I?
| QUOTE (Emc1683 @ Mar 1 2004, 08:38 PM) |
| Silver. |
yeap, your right, took me a while to figure it out, but it has to be silver
To the bold, I am a weapon=Silver Bullet
To the gallant, I am a pin=Silver Star
To the gracious, I am a service=Silver Service???
To the bridesmaid, I am a win=Silver Medal???
To the traitor, I am a bribe=read the bible
To the star, I am a screen=Silver Screen
To the swift, I am an arrow=???????
To the bride, I am a dream=Silver Wedding
I got a riddle....
I'm not racist, I'm black , I have no name but what I was given. As long as I'm turned on no cold no rain no snow will stop me. I'm here to please everyone from America to India?
Who ?????? Answer below
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
Im the XBOX
*head explodes*
What the dirt was that riddle!
Okay, that may have been an easy one, but what about this:
EPISODE XX
My first is double twenty-one but twice of twenty-two,
Decipher it and you will see that statement is quite true.
My next two are just three apart, or, looking at the link,
You'll have the answer easily and will not have to think.
My fourth is so more ways than one, so long as you can spell,
While my fifth splits first and second, so what is it? Can you tell?
It may seem like these words of rhyme are nonsense things to say,
Though the five together are right here (two ways) so what are they?
GOOD LUCK!!!
WORDS
Next!!!!
WORDS is the correct anwser, here's why:
The answer that you seek to find, in words, is now shown here,
To understand the clues read on, I'll try to make it clear.
The twenty-first of letters is U in the alphabet,
Double it, W is the letter you would then get.
Now the twenty-second letter of the alphabet is V,
When written twice together a W it could be.
I hope I've explained the clues to give W as letter one,
Now let's move on, there's four more letters to be done.
The second and third letters are three from each other,
But to scour the alphabet to find them, you needn't bother.
If you were looking carefully you'd have seen in the third line,
The linking word, OR, fits this criteria just fine.
This makes the second O, and R would be the third,
Which gives us W, O and R as letters of this word.
The fourth letter in the alphabet is fourth in the answer too,
Which makes the fourth one D, only one more left to do!
Finally the fifth lies between the first and second,
In the alphabet, S splits W and O, that's what I reckoned.
Combine the five, see that they've been used here a lot?
And in the seventh line, sixth word, the answer even got a spot!
So now you know the answer and those clues are less absurd,
It's amazing what you can do with a word, oops, I mean WORDS!
----------------------------------------------------------------------------
NEXT --- This is an easy one, but sometimes the easiest one is hard to solve! Good Luck!
EPISODE XXI
As far east as east...
As far west as west...
If north is the future
What name fits me best?
bah
Alaska has the western-most point in the U.S. AND the eastern-most point in the United States. This is possible because Alaska straddles the international date line.
Alaska's State motto is: North to the future.
Here's another riddle. Can anyone solve this with the quickness? Good Luck
EPISODE XXII
An iron horse with a flaxen tail.
The faster the horse runs,
the shorter his tail becomes.
What is it?
Heart, Ribs, Lungs, Brain
narator = heart
"they keep me locked up" = ribs/breastbone
"my neighbors import and export" = lungs
"I got a lotta my own connections" = veins and arteries
"The guy upstairs is the boss of it all" = brain
"Hes also incarcerated" = skull
"so long as we get the messages." = nerves/nervous system
thats all i got right now
edit:
"with thousands collectin'" = aveoli (sp?)
"two dozen guards" = ribs
| QUOTE |
EPISODE XXIII
Yeah, they keep me locked up, but I guess Im thankful, in short. I hand out the beatings, while my neighbors import and export. We make a good team, especially me as the muscle, But with two dozen guards, Im glad we never tussle. But really, I got a lotta my own connections, Imports, exports, with thousands collectin'. But between us, theres really no competition, I call it harmonizin cause were on the same mission. No one is unnecessary, or, you know, too small, The guy upstairs is the boss of it all. Hes also incarcerated, but for his good I bet it is, Business is good, so long as we get the messages.
Whos doing the talking, and who are the other players in this riddle? There are a total of 28, not including the narrator. |
Can anyone solve this riddle? I am still waiting to see who can crack this. So far Parrappa and lordvader129 are on the right track, but remember, there's a total of 28. Good luck.
I think I got it all
EPISODE XXIV
You're sitting at a bar, an explosively-dank hole in Funky Town USA.
You have an award that says, most likely to be the character in a riddle . . . looking around your attention finds a small chair with a mobile entity covering it with it's lesser half . . . It speaks, you hear "Glass of water please . . . " You see the bartender examine the seated man for a moment. He then reaches under the counter and pulls out a shotgun point-blank in the man's face. The seated man speaks again "Thank You" he says, and walks out of the bar . . . why did the man get what he needed?
Good luck!
Well a ShotGun would certainly scare the Hiccups right out of me.
So my guess is that he had the hiccups and the shot gun got rid of them but the water might have helped as well.
Saturday: 684/4800
Sunday: 687/4800
Monday: 685/4800
Tuesday: 685/4800
Wednesday: 687/4800
Thursday: 684/4800
Friday: 688/4800
Lol, this math class is boring btw
In a period of 400 years, the cycle of weekdays makes one complete cycle through the years (it cannot be a shorter period because of the odd leap year rule; it does not have to be a longer period because a period of 400 years has 400 × 365 = 146000 normal days plus 100 - 3 = 97 leap days, which makes 146097 days in total, which is divisible by 7). So, we only have to look at the probability in a period of 400 years, for example the years 2001 up to 2400.
For a normal year, the distribution of the 13th days over the days of the week is as follows, if January 13th falls on weekday x:
x x+1 x+2 x+3 x+4 x+5 x+6
2 1 1 3 1 2 2
For a leap year, the distribution of the 13th days over the days of the week is as follows, if January 13th falls on weekday x:
x x+1 x+2 x+3 x+4 x+5 x+6
3 1 1 2 2 1 2
For subsequent years, these distributions shift cyclic 1 place to the right for normal years, and 2 places to the right for leap years.
For three normal years followed by one leap year, we can now calculate the distribution of the 13th days:
x x+1 x+2 x+3 x+4 x+5 x+6
2 1 1 3 1 2 2 (normal year, not shifted)
2 2 1 1 3 1 2 (normal year, shifted 1 place to the right)
2 2 2 1 1 3 1 (normal year, shifted 2 places to the right)
+ 2 1 2 3 1 1 2 (leap year, shifted 3 places to the right)
-----------------------------------
8 6 6 8 6 7 7 (3 normal years and 1 leap year, not shifted)
For four normal years, we find:
x x+1 x+2 x+3 x+4 x+5 x+6
2 1 1 3 1 2 2 (normal year, not shifted)
2 2 1 1 3 1 2 (normal year, shifted 1 place to the right)
2 2 2 1 1 3 1 (normal year, shifted 2 places to the right)
+ 1 2 2 2 1 1 3 (normal year, shifted 3 places to the right)
-----------------------------------
7 7 6 7 6 7 8 (4 normal years, not shifted)
In four years, the latter two distributions shift 5 places cyclic to the right. So for a period of 16 years with 4 leap years, we find:
x x+1 x+2 x+3 x+4 x+5 x+6
8 6 6 8 6 7 7 (3 normal years and 1 leap year, not shifted)
6 8 6 7 7 8 6 (3 normal years and 1 leap year, shifted 5 places to the right)
6 7 7 8 6 6 8 (3 normal years and 1 leap year, shifted 10 places to the right)
+ 7 8 6 6 8 6 7 (3 normal years and 1 leap year, shifted 15 places to the right)
-----------------------------------
27 29 25 29 27 27 28 (16 years with 4 leap years, not shifted)
For a period of 100 years with 24 leap years (the years 2001-2100, 2101-2200, and 2201-2299), we can now calculate the distribution of the 13th days:
x x+1 x+2 x+3 x+4 x+5 x+6
27 29 25 29 27 27 28 (16 years with 4 leap years, not shifted)
29 25 29 27 27 28 27 (16 years with 4 leap years, shifted 20 places to the right)
25 29 27 27 28 27 29 (16 years with 4 leap years, shifted 40 places to the right)
29 27 27 28 27 29 25 (16 years with 4 leap years, shifted 60 places to the right)
27 27 28 27 29 25 29 (16 years with 4 leap years, shifted 80 places to the right)
27 28 27 29 25 29 27 (16 years with 4 leap years, shifted 100 places to the right)
+ 8 7 7 6 7 6 7 (4 normal years, shifted 120 places to the right)
-----------------------------------
172 172 170 173 170 171 172 (100 years with 24 leap years, not shifted)
For a period of 100 years with 25 leap years (the years 2301-2400), we can now calculate the distribution of the 13th days:
x x+1 x+2 x+3 x+4 x+5 x+6
27 29 25 29 27 27 28 (16 years with 4 leap years, not shifted)
29 25 29 27 27 28 27 (16 years with 4 leap years, shifted 20 places to the right)
25 29 27 27 28 27 29 (16 years with 4 leap years, shifted 40 places to the right)
29 27 27 28 27 29 25 (16 years with 4 leap years, shifted 60 places to the right)
27 27 28 27 29 25 29 (16 years with 4 leap years, shifted 80 places to the right)
27 28 27 29 25 29 27 (16 years with 4 leap years, shifted 100 places to the right)
+ 7 8 6 6 8 6 7 (3 normal years and 1 leap year, shifted 120 places to the right)
-----------------------------------
171 173 169 173 171 171 172 (100 years with 25 leap years, not shifted)
Now we can calculate the distribution of the 13th days for the period 2001 up to 2400:
x x+1 x+2 x+3 x+4 x+5 x+6
172 172 170 173 170 171 172 (100 years with 24 leap years, not shifted)
170 173 170 171 172 172 172 (100 years with 24 leap years, shifted 124 places to the right)
170 171 172 172 172 170 173 (100 years with 24 leap years, shifted 248 places to the right)
+ 172 171 173 169 173 171 171 (100 years with 25 leap years, shifted 372 places to the right)
------------------------------------
684 687 685 685 687 684 688 (400 years, not shifted)
Since January 13th, 2001 (x in the distribution) is a Saturday, we get the following probability for the 13th days over the days of the week:
Saturday: 684/4800
Sunday: 687/4800
Monday: 685/4800
Tuesday: 685/4800
Wednesday: 687/4800
Thursday: 684/4800
Friday: 688/4800
Conclusion: the probability that the 13th of a certain month in a certain year is a Friday, is the highest.
Have a nice day...... I do not condone the cheating on homework.