The worlds first riddle!

I think you got it Rap. The forehead's starting to curve again!

1.
4. They both have a vertical axis of symmetry
5. They're both Proper English
6. Page
7. Shhh
8. Tea Tent
10. unite-it=une
11. What?

Rap c∫;?/

Canadian Higher Math Paper Part I (Answers)


1. What letter is nine inches long?
...the letter Y, it is one fourth of a yard (9 inches)

4. Why is the letter A like noon?
.....because it is in the middle of DAY

5. Why is the letter E like London?
.....because it is the capital of England

6. What ends with E and begins with P and has a thousand letters?
.....postoffice

7. How do we know that S is a scary letter?
.....because it makes CREAM SCREAM

8. What starts with T, ends with T, and is full of T?
.....teapot

9. Tommy Tucker took two strings and tied two turtles to two tall trees. How many T's in that?
.....there are 2 t's in THAT

10. From a word of 5 letters, take 2 letters and have 1.
.....ALONE - take the a and the l and you are left with one

11. What letter is most useful to a deaf woman?
.....the letter ?'a' can make 'her' "hear"


Rap: (Nice hat Rap)

School
90students, 4 classes =4*90=360 student classes
15 students, 1 teacher per class, teacher has three classes
360 student classes/15 students=24 classes
3 classes/teacher
24 classes/3 classes/teacher=8 teachers
8 Teachers at the school

Marbles.
So there are 169 marbles
Note this is the minimum number for which this is true
Solutions are j*42+1 where j is an integer >=1

(I urge the reader to check out the full version, a gem)

Goldblat's primes for 36
primes less than 36?-2,3,5,7,11,13,17,19,23,29,31
31+5=36 check
29+7=36 check
23+13=36 check
10+17=36 check
then you start repeating
so there are 4 Goldblat primes for 36

4. They both have a vertical axis of symmetry
5. They're both Proper English
6. Page
7. Shhh
8. Tea Tent
10. unite-it=une
11. What?


Revised Tommy Tucker
2 t's in that


Mark:

2. both are palindromes
5. they're both capitals in England
6. post office
8. teapot
9. 13 if case doesn't matter, otherwise 2
10. prone (are we going to see this one until we exhaust all of the possibilities? ) So you noticed then!


SCHOOL
8 (90*4)/(15*3)

MARBLES
169 LCM(6, 7, 8) + 1

PRIMES
4

"SUM IS 11

10 (What would you say if I suggested 9?)"
"I'd say you're correct, and I should read the questions more carefully. I overlooked omitting your example."

Wait up! You read it here first, "I'd say you're correct" at last, after a lifetime of trying, I finally made it , luck triumphs over brains. :wink:

Whim had a question that morphed into a devil, so I reckon he had a ?'Devil of a question' The answer to which is 42.


French Acadamee Du Science enterence examination.

1. What letters are in; visible, but never out of sight

2. Why should men avoid the letter A

3. Why is the letter F like Paris

4. Why is T the happiest letter of the alphabet

5. Spell mousetrap in 3 letters

6. Why should a boy avoid the letter Y

7. Why are 2 T's like hops

8. Why is the letter U the jolliest letter



It just keeps getting easier.

6, 14, and 15 are factors of the natural number N. What is the smallest value that N can have


Mark and Rap each shot 6 arrows at the target. Mark shot 4 arrows into A and 2 into B; his score was 18 points. Rap shot 3 into A and 3 into B; his score was 21 points. How many points were given for an arrow in B


When a natural number is multiplied by itself, the result is called a perfect-square. Since 1x1 = 1, 2x2 = 4, 3x3 = 9 and so forth, 1, 4, 9 and so forth are perfect-squares. What year in the 18th century (the years 1701 through 1800) was a perfect square


List all of the different natural numbers that each leave a remainder of 2 when divided into 83

Because Francis lives there?

[size=7]1. S and I
2. because it can make them mean
3. it's the capital of France
5. cat

FACTORS
210

ARROWS
5

83
3^N, 1 <= N <= 4

SQUARE YEAR
1764


"Marbles.
So there are 169 marbles
Note this is the minimum number for which this is true
Solutions are j*42+1 where j is an integer >=1"

If that were true, then 169 wouldn't be the answer.
Solutions are j*168+1 where j is an integer >= 1.[/size]

[size=7]1) VBLE
2) Puts them in a high draft classification
3) Capitals
4) It's at the end of a R_ST.[/size]

Smallest Factor
[size=7]6=2*3
14=2*7
15=3*5
so LCM is 2*3*5*7=210[/size]

Arrows
[size=7]]4A+2B=18 or 2A+B=9
3A+3B=21 or A=B=7
so A=2 and B=5
B=5[/size]

Square Number
[size=7]1701<=n^2<=1800
so n=42 and
n^2=1764[/size]

Natural #'s
[size=7]83 is prime
so n=82*i+2 fir integer i>=0
2 is the smallest number since
2/83=0R2
the next is 85[/size]

Rap c∫;?/

French Acadamee Du Science enterence examination.

Answers translated by Francis.

1. What letters are in; visible, but never out of sight?
.....s and i

2. Why should men avoid the letter A?
.....because it can make men mean

3. Why is the letter F like Paris?
.....because both are the capitol of France

4. Why is T the happiest letter of the alphabet?
.....because it is next to U

5. Spell mousetrap in 3 letters.
.....c-a-t

6. Why should a boy avoid the letter Y?
.....it can turn a lad into lady

7. Why are 2 T's like hops?
.....because they make beer better

8. Why is the letter U the jolliest letter?
.....because it is in the middle of fun


(Why is the letter F like Paris?)
Francis wrote, "Because Francis lives there?"

Francis, you do make me laugh.

Mark:

1. S and I
2. because it can make them mean
3. it's the capital of France
5. cat

FACTORS
210

ARROWS
5

83
3^N, 1 <= N <= 4 (You could have said a simple : 3, 9, 27, and 81.)


SQUARE YEAR
1764


"Marbles.
So there are 169 marbles
Note this is the minimum number for which this is true
Solutions are j*42+1 where j is an integer >=1"

If that were true, then 169 wouldn't be the answer.
Solutions are j*168+1 where j is an integer >= 1.

Seen and notediddley noted. Re-Dots: The report was in the Oct 27th 2004 Edition of Science News.


Rap:

1) VBLE
2) Puts them in a high draft classification
3) Capitals
4) It's at the end of a R_ST.

Smallest Factor
6=2*3
14=2*7
15=3*5
so LCM is 2*3*5*7=210

Arrows
]4A+2B=18 or 2A+B=9
3A+3B=21 or A=B=7
so A=2 and B=5
B=5

Square Number
1701<=n^2<=1800
so n=42 and
n^2=1764

Natural #'s
83 is prime
so n=82*i+2 fir integer i>=0
2 is the smallest number since
2/83=0R2
the next is 85 Hello, Earth to Rap....


Easy, was yesterday. Today, we get down and dirty.

How thick can I get: (Hang on, does that sound right?)

Fold a piece of paper in half. It is now twice as thick as it was. Fold in half again. Now it is four times as thick as the original unfolded sheet.
Continue folding the paper in half. Do you find that it is difficult to go much further? You could try a larger piece of paper. However, you will still find it difficult to continue folding it in half.

Imagine that you did not have this limitation and that you could take a very large piece of paper and fold it in half 50 times. How thick would it be


Before you try to calculate the result, take a guess as to about how thick you think it would be. How does your calculation compare with your guess



The average of six numbers is 7. If two of the six numbers are removed, the average of the remaining numbers is 8. What is the sum of the two numbers which were removed


N is the 5-digit number 8A65B in which A and B are digits, and N is divisible by 24. What is the smallest number N can be


If a class of children is separated into groups of 5 children, 2 children will be left over. If the class is separated into groups of 6 children, 3 children will be left over. What is the smallest number of children the class could have


A natural number is a multiple of 13 and is also divisible by 4 and by 6. What is the smallest number that satisfies these conditions


Eight people want to play a 48-minute game as a team but only a team of exactly five is allowed to play. However, during the game, a player may be replaced by someone else. Suppose each of the eight people plays in the game for the same amount of time. How many minutes will each of the eight people play


Spanish Civil Service Vet examination.

1. What animal drops from the clouds
2. What animal doesn't play fair
3. Why did the chicken cross the playground
4. What do bees do with all their honey
5. What is the principal part of a horse
6. What do people in Spain call little gray cats
7. What makes a Dalmatian dog spotted
8. What bird can lift the heaviest weight
9. When is a dog's tail not a dog's tail
10. How do we know that one bird is insane

[size=7]PAPER
2^50 times as thick as the original sheet

TWO NUMBERS
10

5-DIGIT NUMBER
82656

CHILDREN
27

NATURAL NUMBER
156

GAME
30 minutes

SPANISH EXAM
1. cats and dogs
6. gatos[/size]

1. What animal drops from the clouds?

.....the rein,dear

2. What animal doesn't play fair?

.....the cheetah

3. Why did the chicken cross the playground?

.....to get to the other side

4. What do bees do with all their honey?

.....they Cell it

5. What is the principal part of a horse?

.....the mane part

6. What do people in Spain call little gray cats?

.....little kittens

7. What makes a Dalmatian dog spotted?

.....his spots

8. What bird can lift the heaviest weight?

.....the crane

9. When is a dog's tail not a dog's tail?

.....when it's a waggin'

10. How do we know that one bird is insane?

.....because it is always a raven

1) Dogs & Cats
2) Cheetah
3) It thought it was a road

Paper Thickness
[size=7]50 folds will result in 2^(50-1) plies of paper. 2^(50-1) is a really big number(~5.6x10^14)[/size]

Less Two
[size=7]SumX8/8=7 SumX8=56
SumX6/6=8 SumX6=48
SumX2=SumX8-SumX6=56-48=8[/size]

Missing Digits
[size=7]24=2^3*3 so B=6, through manipulation A=2,5,8
Smallest number is 82656 A=2, B=6[/size]

Class Division
[size=7](n)mod5=2
(n)mod6=3
n=25+2=27
n=24+4=27
class has 27 students[/size]

Least Common multiple
[size=7]3,4,13 are mutually prime, so N=3*4*13=156[/size]

Game
[size=7]5*48/8=5*6=30
So each player can play for 30 minutes[/size]

Rap c∫;?/

For Spanish Exam results check out the answers from Francis.

Chicken in playground, ?'To get to the other Slide'




Mark: (To err is human) :wink:

PAPER
2^50 times as thick as the original sheet

TWO NUMBERS
10

5-DIGIT NUMBER
82656

CHILDREN
27

NATURAL NUMBER
156

GAME
30 minutes

SPANISH EXAM
1. cats and dogs
6. gatos (Mark you're an ace)



The smart Rap twin:

PAPER
2^50 times as thick as the original sheet



Paper Thickness
50 folds will result in 2^(50-1) plies of paper. 2^(50-1) is a really big number(~5.6x10^14)





How Thick Does it Get?

Let's look at the pattern we get by folding. After the first fold, the result is 2 sheets thick. After the second fold it is 4 sheets thick, then 8, then 16 and so on:

2, 4, 8, 16…

This sequence may be written as powers of 2:

21, 22, 23, 24,…

If we fold 50 times the thickness of the final result is 250 sheets. How thick is this?

We measured the thickness of a one ream package of paper we had here in the office. It was 5 cm thick. Since there are 500 sheets in a ream, each sheet is 0.01 cm thick.

Now 250 is a very large number. It equals 1.1259 X 1015. This may also be written as

1,125,900,000,000,000

That's a very thick pile of paper! Since each sheet is 0.01 cm thick we can divide our result by 100 to find out how high it is in centimetres:

11,259,000,000,000 cm

It's still hard to imagine how big this is, so let's divide by 100 again to convert to meters:

112,590,000,000 m

Maybe we should try kilometres. There are 1,000 meters in a kilometre, so dividing by 1,000 we have:

112,590,000 km

The distance from the earth to the sun is about 150,000,000 km.



We return to the second grade.

Could you work for NASA? Get this wrong and a lot of folk are gonna fry.

Two missiles are 148,148 kilometers apart aimed directly at each other.
I shout FIRE...
One is traveling at 38,000 kilometers per hour. The other is going 22,000 kph.

How far apart are they ?'one minute' before the collision




A number is greater than IO and has the property that, when divided either by 5 or by 7, the remainder is 1. What is the smallest odd counting number that has this property


Find the greatest number that divides 364, 414, and 539 with the same remainder in each case


In a group of 5 children, the average weight of each child was 72 pounds. When a sixth child joined the group, the average weight of each child became 73 pounds. What was the weight of the sixth child


Four numbers are arranged in order of size and the difference between any two adjacent numbers is the same. Suppose 1/3 is the first and 1/2 is the fourth of these numbers. What are the two numbers between 1/3 and 1/2


The product of two numbers is 504 and each of the numbers is divisible by 6. However, neither of the two numbers is 6. What is the larger of the two numbers


The Australian Higher Examination.

1. What is it that everyone always overlooks
2. What is always before you, yet you can never see it
3. What can be right but never left
4. What is full of holes and yet holds water
5. What is it that we often return but never borrow
6. With what do you fill a barrel to make it lighter than when it is empty
7. What is always coming but never arrives
8. What increases the more you share it with others
9. What is bought by the yard and worn by the foot
10. What is broken when you hear it

Missiles
[size=7](38,000+22,000)/60=60,000/60=1000 km
one minte before they're 1000 km apart[/size]

Greater than 10
[size=7]nmod5=1, nmod7=1
n=5*7+1=36[/size]

Greatest divisor
[size=7]364modn=414modn=539modn
n=5, 5*5
larger of two is 5*5=25[/size]

Rolly Polly
[size=7]SX5=5*72 SX6=6*73 X=6*73-5*72=72+6=78
Sixth kid weighs 78 pounds[/size]

Ordered Numbers
[size=7]d=a+3n=1/3+3n=1/2
n=1/18
a=6/18=1/3
b=7/18
c=8/18=4/9
d=9/18=1/2
ordered quatrain
1/3, 7/18, 4/9, 1/2[/size]

Find the number
[size=7]a*b=504
a=n*6, b=m*6
n*m=504/(6*6)=14
n=2, m=7
a=2*6=12
b=7*6=42
so the factors of 504 are 12 & 42[/size]

1)?
2) Air
3)?
4) Sponge Bob
5) Vengeance
6) Hydrogen, Helium, or Hot Air
7) Tomorrow
8) Favors
9) Carpeting, Sod
10) Wind---oops I farted

Rap c∫;?/

[size=7]MISSILES
1000km (no matter how far apart [>1000km] they were to begin with

5 AND 7
71

364, 414, AND 539
25

CHILDREN
78

FOUR NUMBERS
7/18 and 4/9

TWO NUMBERS
42

AHE
1. Their noses
2. tomorrow
3. a whale, an angle
5. a compliment
7. tomorrow[/size]

Odd number odd number

nmod5=1
nmod7=1
nmod2=1
then
n=(2*5*7)+1=71

A steeper differential of my forehead again!

Rap c∫;?/

The Australian Higher Examination. Answers.

1. What is it that everyone always overlooks?
.....one's nose

2. What is always before you, yet you can never see it?
.....your future

3. What can be right but never left?
.....a right angle

4. What is full of holes and yet holds water?
.....a sponge

5. What is it that we often return but never borrow?
.....thanks

6. With what do you fill a barrel to make it lighter than when it is empty?
.....holes

7. What is always coming but never arrives?
.....tomorrow

8. What increases the more you share it with others?
.....joy

9. What is bought by the yard and worn by the foot?
.....carpeting

10. What is broken when you utter it?
.....silence


NASA is grateful for your assistance leading to a safe and successful launch.

I note no one was fooled by the start distance.


Rap: (Return to the vertical)

?'Show me a man who has never made a mistake, and I will show you a man who has never made anything'. :wink:

Missiles
(38,000+22,000)/60=60,000/60=1000 km
one minute before they're 1000 km apart

Greater than 10
nmod5=1
nmod7=1
nmod2=1
then
n=(2*5*7)+1=71

Greatest divisor
364modn=414modn=539modn
n=5, 5*5
larger of two is 5*5=25

Rolly Polly
SX5=5*72 SX6=6*73 X=6*73-5*72=72+6=78
Sixth kid weighs 78 pounds

Ordered Numbers
d=a+3n=1/3+3n=1/2
n=1/18
a=6/18=1/3
b=7/18
c=8/18=4/9
d=9/18=1/2
ordered quatrain
1/3, 7/18, 4/9, 1/2

Find the number
a*b=504
a=n*6, b=m*6
n*m=504/(6*6)=14
n=2, m=7
a=2*6=12
b=7*6=42
so the factors of 504 are 12 & 42


Mark:
MISSILES
1000km (no matter how far apart [>1000km] they were to begin with

5 AND 7
71

364, 414, AND 539
25

CHILDREN
78

FOUR NUMBERS
7/18 and 4/9

TWO NUMBERS
42


Let's nail the numbers for this once and for all.

How many people do you think there would have to be in a room to have a better than even chance that at least two people share a birthday?
In other words, how many people do you need for the probability of a shared birthday to be greater than 50%

How many people do you need for the probability to be greater than 90%


To start with you have two cans of juice. What is the probability that you will guess correctly (Since this is a math puzzle, let's assume that you really can't taste the difference so you are just making random guesses.)
With three cans, what's the probability of guessing all of them correctly

What if there are four cans of juice
How about 10
How about 100

Can you come up with a general formula for the probability of guessing all the flavors correctly with N cans of juice



When the order of the digits of 2552 is reversed, the number remains the same. How many counting numbers between 100 and 1000 remain the same when the order of the number's digits is reversed


Whim shot 3 arrows; 2 landed in the A ring and 1 landed in circle B for a total score of 17. DrewDad also shot 3 arrows; 1 landed in A and 2 in B for a total score of 22. How many points are assigned to Circle B


If a is divided by b, the result is 3/4. If b is divided by c, the result is 5/6. What is the result when a is divided by c


T and V in the four-digit number T37V represent different digits, and T37V is divisible by 88 without remainder. What digit is represented by T

[size=7]BIRTHDAYS
Assuming 365 days in a year, 23 and 41.

JUICE CANS
2: 1/2
3: 1/6
4: 1/24
10: 1/10!
100: 1/100!
N: 1/N!

REVERSED DIGITS
90

ARROWS
9

ABC
5/8

TV
2[/size]

Birthday Odds
[size=7]This is a reversal problem--first you have to figure the probability of none of them share a birthday and subtracting this probability from certainty. The result, one birthday (or more) shared
P(E)=50% E is about 22
P(E)=90% E is about 40
I've always heard it is a safe bet at 30. This is where the P(E) is about 72%[/size]

Juice Flavor
[size=7]I think there something missing here Try, perhaps your forehead has an increasing gradient too?[/size]

Palindrome numbers between 100 and 1000
[size=7]Including 101 and 999 there are 90[/size]

Whim and Drewdad's arrows
[size=7]2A+B=17
A+2B=22
3B=27 B=9[/size]

a/c
[size=7]a/b=3/4
b/c=5/6
a/c=a/b*b/c=3/4*5/6=15/24=5/8[/size]

T&V
[size=7]T37V=2376
2376/88=27
T=2[/size]

Rap c∫;?/

Hi Peoples!

I can see that I've been missing all the fun! Just got back from a week of cliff hanging thrills in the Pyrenees. It was mad fun!

With the juice cans......Are there just 3 juice cans, or are there three different flavors of juice?

If just 3 cans, and only one can of each flavour....the odds are better.
Or are all cans independant, and all could be lemon, or all be orange.

first scenario...only 3 cans of each....1/7
second scenario (random).....1/14

Cans of Juice

This is the same as picking N objects out of N at random-I guess.

If N=2 then the odds of getting N correct is 1 out of 2 . The combinations are both all correct or both wrong (1/2).

Note---it is impossible to get N-1 right. If you've got N-1 out of N right the Nth will also be right.

if N is 3
then the possibilities are 1 correct two wrong, all correct, or all wrong (1/3)
combinations are
3!/((3-3)!3!)+3!/((3-1)!1!)+3!/((3-0)!0!)=1+3+1=5
all correct 1/5
one correct 3/5
all wrong 1/5

if N=4, all correct, 1 correct, two correct, or all wrong or 1 out of 4
1+4+6+1=12
all correct 1/12
one correct 1/3
two correct 1/2
none correct 1/12

if N=10 then it will be all, 1,2,3,4,5,6,7,8, and none correct
the combinations are
1+10+15+120+210+234+210+120+15+1= 936
all correct 1/936
1 correct 5/468
2 correct 5/312
3 correct 5/39
4 correct 35/156
5 correct ¼
6 correct 35/156
7 correct 5/39
8 correct 5/312
none correct 1/936

As for 100 this is tedious to do by hand, however a general solution exists?-I just don't know how to do it on paper rather than at syndications of gear heads.

N see answer to N=100

Rap c∫;?/