The worlds first riddle!

Do you know your ABC?

ABCE is an isosceles trapezoid and ACDE is a rectangle. AB = 10 and EC = 20. What is the length of AE


In the given figure, PA and PB are tangents to the circle at A and B respectively and the chord BC is parallel to tangent PA.

If AC = 6 cm, and length of the tangent AP is 9 cm, then what is the length of the chord BC

ISOSCELES TRAPEZOID
AE = 10 (similar triangles - drop altitude from A to EC)[/size]

[size=8]TANGENTS
BC=4 (similar triangles again - APB and CAB are similar)[/size]

[size=8]33-73
And a few puzzles further back, 77 was shown to not possess this property. You were going to see if you had the proof that 77 is the largest such number.

THREE CARDS
There are C(52,3) ways to choose three cards. There are 4^3 ways to choose a king, a queen, and an ace.
Therefore, the probability is 0.017+.[/size]

Mark:

33-73
And a few puzzles further back, 77 was shown to not possess this property. You were going to see if you had the proof that 77 is the largest such number.

(The best I have found is a site that states: "77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1." There is no other mention)


THREE CARDS
There are C(52,3) ways to choose three cards. There are 4^3 ways to choose a king, a queen, and an ace.
Therefore, the probability is 0.017+.




I am confident that I have never asked this question during the last 24 hours.

A number of cats got together and decided to kill between them 999919 mice.

Every cat killed an equal number of mice.

Each cat killed more mice than there were cats.

How many cats do you think there were

[size=8]CATS
Since the only factors of 999919 are 991 and 1009, there must have been 991 cats.[/size]

Mark:

CATS
Since the only factors of 999919 are 991 and 1009, there must have been 991 cats.

(There must indeed)

Mark, I can't help but notice you somehow look different, Have you changed your hairstyle?




"I am like so mad at you two for hanging round that Halle Berry tramp," said Shari in a tone that could cut steel. However, if you can help me with this last crossword clue I will give you a big surprise.


The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten's place of the original number is equal to twice the difference between its digits.

What the heck is that number



"Don't forget my clue," said Butterfly.
If Log2 x - 5 Log x + 6 = 0, then what would the value / values of x be



Try was about to say something smart, when he was stopped by Mark who had this swell idea.

[size=8]SHARI'S NUMBER
46

BUTTERFLY'S NUMBER
Assuming that is log2(x) and not log(2x), the answer is
3762.982[/size]

Oh, I'm wearing my hair longer than usual in this picture.

RECTANGLE TILING REVISITED

The dimensions are:
1: 1x14
2: 5x7
3: 8x10
4: 4x6
5: 2x15
overall: 9x25

"RECTANGLE TILING REVISITED"

Mark, you are a wizard, the perfect solution.



A wizard named Mark says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old."

How old is Mark

[size=8]WIZARD
360[/size]

Mark:

SHARI'S NUMBER
46

BUTTERFLY'S NUMBER
Assuming that is log2(x) and not log(2x), the answer is
3762.982

WIZARD
360



A certain type of mixture is prepared by mixing brand A at Rs.9 a kg., with brand B at Rs.4 a kg. If the mixture is worth Rs.7 a kg., how many kgs., of brand A are needed to make 40kgs., of the mixture



One dog tells the other that there are two dogs in front of him. The other one shouts that he has two behind him. What is the minimum number of dogs




In an effort to diet, Mark ate 100 bananas in five days, each day eating six more than the previous day. How many bananas did he eat on the first day

[size=8]MIXTURE
24 kg

DOGS
4

BANANAS
8[/size]

Mark:

MIXTURE
24 kg

DOGS
4

(Sorry dude, three will meet the conditions)

BANANAS
8




If it takes Butterfly five minutes to boil one egg, how long will it take Shari to boil 111 eggs


The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose


Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9. She whispered and I will float your boat

DOGS
oops

[size=8]EGGS
Not enough information.

CLOCK
The clock gains 6/11 hours.

SOLVE FOR X, Y
x = 3/2, y = 3
x = -3, y = -3/2[/size]

I'm in Chicago until Thursday afternoon. It's muggy.

Mark:

CLOCK
The clock gains 6/11 hours.

I have: 32 8/11 minutes. We cannot both be right.

SOLVE FOR X, Y
x = 3/2, y = 3
x = -3, y = -3/2


Mark wrote, "I'm in Chicago until Thursday afternoon."

Don't tell me another year has passed, where did the time go? Oh, well, I should have guessed when Shari packed her Darth Vader mask.
Have a good time at the Star Wars convention.

For the rest of us, how about a trip down memory lane:


What is the only word in the English language that when capitalized is changed from a noun or a verb to a nationality


I have keys that open no locks, I have space, but there is no room, You can enter, but you can't go in. I am



Mr. and Mrs. Butterfly have six daughters and each daughter has one brother. How many people are there in the family

"I have: 32 8/11 minutes. We cannot both be right."
Sure we can - they're equivalent.

Star Wars
You ninny - it's Star Trek.

[size=8]KEYS
a keyboard

BUTTERFLY FAMILY
nine[/size]

"I have: 32 8/11 minutes. We cannot both be right."
Sure we can - they're equivalent.


Stone me! You are right. How about that, miracles do happen.





Star Wars
You ninny - it's Star Trek.

Apologies, I defer to your in depth Trekkies knowledge. Have a good time and say hi to Yoda you can.