The worlds first riddle!

disappearing words:
$300
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It is with expediency born from pragmatism as I wish to avoid being categorized as a melodramatic egomaniac, but political correctness dictates that I confirm the answer crafted by none other than Mark.

A2K Riddles club:
With 50% more to share the expense, the cost per person would have been 2/3 as great.
Thus $100 is one-third and the initial individual cost was $300.


Al and Billie-Dee Zaster have five kids, Christine, Daniel, Elizabeth, Fredrick and Grace.

Al decided that he would like to determine a cycle of seating arrangements at their circular dinner table so that each person would sit by every other person exactly once during the cycle of meals.

How did he do it, or is it even possible?

Here's one way:
abcdefg
acegbdf
adgcfbe
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Mark, I’m not sure about your third: adgcfbe

Although he correctly identified that there were three meals in the cycle.

Missy thought they rode 7 miles on their bicycles – Close enough sweetie.

Here’s how I have it:
There would be 6/2 or 3 distinct pairs with which to bracket Al, so there must be 3 meals in a cycle.

Using the initials of the names, let us first seat the family in alphabetical order and then break the circle at Al’s right and straighten out the sequence for consideration.

Then take those in an even position and move them to the right, preserving their order and repeat the operation twice.
The third move returns the seating to the original alphabetic order.

Thus,
A B C D E F G
A C E G B D F
A E B F C G D

A B C D E F G

Now let us examine the bracketing pairs for each person, and incidentally demonstrate that the device used does the job.




Three city cops went to a sleazy diner (dirty, but cheap). The first cop bought four sandwiches, a cup of coffee and ten doughnuts (he was on a diet) for $1.69.

The second purchased three sandwiches, a cup of coffee and seven doughnuts for $1.26.

My question is two-fold: What is the name of the first cop’s wife and-
What did the third cop pay for a sandwich, a cup of coffee and a doughnut?


Ima plannin’ going down Springfield ways to do me some hog wrasslin' and those lil greased gal’s sure do take some catchin’, so take your time chewing over the problemo.

cops:
1) ?
2) 40 cents
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Mark:
Pity you don’t know her name because she was hot! I guess her address is outta the question too.

Two: Correct.


This one is a real doozy…

Snake weighs half as much as Moe and John weighs three times as much as Snake.

Together, they weigh 720 pounds.
How much does each man weigh?

Snake: 120 lbs
Moe: 240 lbs
John: 360 lbs

how do you know sweetie is spelled with an ie and not with a y?

I always pass on good advice. It is the only thing to do with it. It is never of any use to oneself.

Oh Missie, it is for the same reason I Googled, "Missing medieval servant".
It came up with, "Page not found".

Mark may be a genius, but you were the only one to know the answer to the question: What's long, hard and has cum in it?



You were quite right, it was - a cucumber!

Did you know I dreamt of you the other night; you were in the bathroom taking a shower and I was gonna do the Alfred Hitchcock. ... Psycho thing with the shower curtain an all….

When all of a sudden a strange family came into the room and started showing us photographs. You got out and sat in the tub just wearing a towel!!!

I must stop eating cheese just before I go to bed.

However to answer your question... I'd like to defend a penguin in court just to say, "Your Honour, my client is clearly not a flight risk."


BTW, I won’t stop praying for your Pa’s full recovery till the Yankees win the pennant!

It would appear that Mark is the only person in the universe who knows all the boys…

If Moe weighs twice as much as Snake, and John three times as much, dividing their total weight by six gives us Snake's weight (think x + 2x + 3x = 720).
720 divided by 6 tells us that Snake weighs 120 pounds, so Moe weighs 240 pounds and John weighs 360 pounds.

As y’all may know, boxing is my passion….


I can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, I sent a total of 96 boxes.

If there are more large boxes than small boxes, how many cartons did I ship?

Boxes - Two possibilities:

11: 7 cartons of 56 large boxes and 4 cartons of 40 small boxes
12: 12 cartons of 96 large boxes (96 > 0)

Thank you for you well wishes for ma pa. Been reading my blog again I see.

Have a good weekend you.

Mark enlightened us with:
Boxes - Two possibilities:

11: 7 cartons of 56 large boxes and 4 cartons of 40 small boxes
(That is what I have)

But to me the second is far more interesting.
12: 12 cartons of 96 large boxes (96 > 0)

That is something I never thought of; way to go Mark (and Mimsea, who I’m sure is way ahead of the game).

Ok, I have sum revision this weekend, so I leave you with the following brain teasers…

a) If f (x) = x10 + x8 +x6 + x4 + x2 + 1, and your life depended on it; could you show that f (2i) is divisible by 9?

Show and tell ; nein.
b) Can you possibly show that each member of the infinite series 1, 11, 111, 1111, . . .
Is a triangular number in the scale of notation with base nine?


Missee, “Have a good weekend you.”
Right backatya girlie.

a)
f(2i) = -1024 + 256 - 64 + 16 - 4 + 1 = -819 = -91 * 9

b)
(1) If T is a triangular number, then 9*T+1 is a triangular number.
(2) Each member (after the first) of the base 9 infinite series 0, 1, 11, 111, ... is 9 times the previous member plus 1.
(3) 1 is a triangular number.
Therefore, by induction, all members of the base 9 infinite series 1, 11, 111, ... are triangular numbers.

Justification for (1)
All triangular numbers can be expressed as x*(x+1)/2 for some integer x >= 0.
All numbers of the form x*(x+1)/2, for integer x >= 0, are triangular numbers.
x*(x+1)/2 is an arbitrary triangular number.
9*x*(x+1)/2 + 1
= (9*x*(x+1)+2)/2
= (9x^2 + 9x + 2)/2
= (3x+1)*(3x+2)/2
= (3x+1)*((3x+1)+1)/2
= y*(y+1)/2 where y = 3x+1
Therefore 9*x*(x+1)/2 + 1 is triangular.

Justification for (2)
Just as multiplying a base 10 number by 10 is equivalent to appending a 0 to the right of the original number, multiplying a base 9 nuumber by 9 is equivalent to appending a 0 to the right of the original number (this is true for any base). Given a string of N 1s, multiplying it by 9 gives a string of N 1s followed by a 0. Adding 1 to this give a string of N+1 1s.

As we all know - Light travels faster than sound.

This is why I appear bright until you hear me speak; so I will remain silent and urge y’all to note Mark’s remarkable answers – you’ll never see better.

It is well known down at the funny farm that I’m never wrong. Except the one time I thought I was wrong, but I was wrong about that…

So if I said that if the top 26 cards of an ordinary deck contain more red cards than there are black cards in the bottom 26, then there are in the deck at least three consecutive cards of the same color.

Would I be wrong?

Cards:
No, an if-then statement is false only if the antecedent is true and the consequent is false. Since the number of red cards in the top half of the deck must equal the number of black cards in the bottom half of the deck, your antecedent is false. Therefore, your statement is true independent of whether or not there are at least three consecutive cards of the same color in the deck.
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This is what I need to learn to do.

Hi mismi
Sorry blue guy, nothing to do with you. Just wanted to see the sun.

Hiya ttl

Where is you Tryagain? You have been away for 3 months. That silent thing - you were serious eh?

Why has he been gone for 3 months? Did something happen to him?