The worlds first riddle!

Z = 6
7*95238 = 666666

btw, TA, i like my answer of bowling ball better than rear wheel, because rear wheel can go backwards, for example when a car is in reverse.

My great grandfather and my father differ as much in age as my grandfather and me. My great grandfather is 27 years older than my grandfather.
How much differ my father and me in age?

Explain how you arrive at you answer.

Whim

ABC+DEF+GHI=JJJ
J=9

BETS
You are Molly
Waldo started with 30 cents
Spike started with 40 cents

PYRAMID
I think we need to know the area of the base. Or are we to figure out the largest pyramid that can be completed before the work force is exhausted?

Assuming the latter, it will take 53 days to build a pyramid 46 levels (138m) high. If a crew member dies whether or not his crew layed a block, then 1416 survive. Otherwise, since only 15 blocks are layed the last day, 1489 would have survived.

PHONE NUMBER
There are two solutions without leading zeros in either the dividend or the divisor:
879-9912 and 989-9901

PRODIGITIOUS
I already answered this last December, so I'll leave it for others.

CANDY
I gave up the first time this was posted, and I'll give up again. I did take a peek at the answer to remind myself why I never would have gotten it.

BY THE WAY
13/6 = 2 1/6

GGF - F = GF - M ---> GGF - GF = F - M
GGF - GF = 27
Therefore F - M = 27

Panic over.

This is what I have for the ?'Foil':
The volume formula for a right parallelepiped is needed: volume = height • width • length or : V = a • b • c . Since the length is wanted, the formula must be changed to: length c = V : a: b or c = V: (a • b). Now V must be calculated with the formula: mass = volume • density or: m = V • ρ (rho), changed to: V = m: ρ . With: V = 1 kg : 2.7 kg/dm³ = 0.37 dm³ = (1 dm = 100 mm , therefore 1 dm³ = 100 mm • 100 mm • 100 mm = 1,000,000 mm³ ) 0.37 • 1,000,000 mm³ = 370,000 mm³. Thus c = 370,000 mm³ : (0.06 mm • 297 mm) = 370,000 mm³ : 17.82 mm² = 20,763 mm = 207.63 m .

Mark, "BY THE WAY 13/6 = 2 1/6"

How strange I read it as 13/16. Get with the programme, and new glasses. I am going for a lie-down.

While we are at it;

Yitwail, "i like my answer of bowling ball better than rear wheel, because rear wheel can go backwards"

So, I believe can a bowling ball. Surely all balls start with reverse spin. Unless you are bowling ?'overhand'. What do others think?

"So, I believe can a bowling ball. Surely all balls start with reverse spin. Unless you are bowling ‘overhand’. What do others think?"

Good bowlers put lots of spin on the ball, and the ball (first of a frame when all ten pins are up) almost never goes straight.

FOIL
20,763mm = 20.763m (better go for another lie-down :wink: )

good point on spin; but when shooting spares, maybe spin is omitted? i'm no bowler of any sort, so this is mere speculation.

Mark

Mark: (Hail the all conquering hero)

ABC+DEF+GHI=JJJ
J=9


Since there are no leading zeros, J must be 7, 8, or 9, since JJJ = ABC + DEF + GHI ≥ 100+240+350 = 690. Now, the remainder left after dividing any number by 9 is the same as the remainder left after dividing the sum of the digits of this number by 9. Next note that 0 + 1 + ... + 9 has a remainder of 0 after dividing by 9, and since JJJ has a remainder of 0, 3, or 6, it follows that J must be 9, since it's the only number from 7, 8 and 9 that leaves a remainder of 0, 3, or 6 if you remove it from the sum 0 + 1 + ... + 9.


BETS
You are Molly
Waldo started with 30 cents
Spike started with 40 cents


Let Waldo start with w, Molly with m, and Spike with s. Following the above account we get the following progression of monies:
• W = 2*w, M = m-w
• M = 2*(m-w), S = s-(m-w) = s+w-m
• S = 2*(s+w-m), W = 2*w-(s+w-m) = w+m-s
And so Waldo finished with w+m-s, Molly with 2*(m-w), and Spike with 2*(s+w-m). Since these must all be equal, we have three equations and three unknowns, so solve; this gives us that 4*m = 5*s and 3*s = 4*w. Now, if s = 1/2 this implies that w = 3/8 = 37.5 cents, an impossible amount of money to start with. If w = 1/2 this implies that s = 2/3, again an impossible amount to start with. Finally, if m = 1/2 this implies that s = 2/5 = 40 cents, w = 3/10 = 30 cents, which works. It follows that I am Molly.


PYRAMID
I think we need to know the area of the base. Or are we to figure out the largest pyramid that can be completed before the work force is exhausted?

Assuming the latter, it will take 53 days to build a pyramid 46 levels (138m) high. If a crew member dies whether or not his crew layed a block, then 1416 survive. Otherwise, since only 15 blocks are layed the last day, 1489 would have survived.



Each block added results in the death of exactly one slave, and when there are less than 17 slaves no more blocks may be added, so the pyramid consists of at most 35000-16 = 34984 blocks. The first level needs 1 block, the next 4, and in general the ith level requires i^2 blocks, and so a pyramid n levels tall requires 1 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6 blocks. This is between n^3/3 and (n+1)^3/3, and solving n^3/3 = 34984 we get that the maximum number of levels is either 46 or 47, with a quick check showing that 46 is correct.

It follows that the pyramid is 46*3 = 138 meters tall, consists of 33511 blocks, and the number of slaves surviving the construction is 35000-33511=1489.
To compute the number of days required for construction, note that if there are m slaves on a given day the number of blocks added is between m/17 and m/17 - 16/17, and given k days it can be easily shown that the number of blocks added is between m/17 + (16/17)m/17 + ... + (16/17)^{k-1} m/17 and m/17 + (16/17)m/17 + ... + (16/17)^{k-1} m/17 - k*16/17; summing the geometric series we get m*(1-(16/17)^k), and so to find the number of days required we solve 35000*(1-(16/17)^k) = 33511 and get that (16/17)^k = .04254 or k=52.08.

Since this came from an upper bound on the number of blocks, it's a lower bound on the number of days; thus, it'll take at least 53 days to build the pyramid. Checking the lower bound, we see that the number of blocks that can be added in 53 days is greater than 33542, and so the pyramid can indeed be built in 53 days.



PHONE NUMBER
There are two solutions without leading zeros in either the dividend or the divisor:
879-9912 and 989-9901




PRODIGITIOUS
I already answered this last December, so I'll leave it for others.

No way will that question ever be answered again. Far too difficult.


Mark proving what a foil I am writes, "20,763mm = 20.763m (better go for another lie-down"

Hey! I'm already horizontal. I am ?'working' under difficult conditions here!


Yitwail, "but when shooting spares, maybe spin is omitted"


OK! OK! You win. When ?'shooting spares' if asked the answer to that riddle it is as you gave. However, at all other times it is as stated. :wink:

Scheesh, the next thing we will be discussing is; what proportion of a ball's travel is ?'slide' before forward revolution takes over?



Whim, good problem. Mark made it look easy, but if you saw all my scribbles it was anything but.






Classic Riddles

1. Think fast: There's an electric train traveling south. The wind is from the north-west. In which direction would the smoke from the train be blowing

2. What is the second most used letter in the English language
Hint: it is also the first letter of the most used word in the English language.

3. In an unabridged dictionary, what 3 letter word has the most definitions

4. How can you avoid hitting your fingers when driving in a nail with a hammer

5. Why did the bubble gum cross the road

6. What walks on 4 legs in the morning, 2 legs in the afternoon, and 3 legs in the evening

7. What 5 letter word can have its last 4 letters removed and still sound the same

8. If you see a bird sitting on a twig, how could you get the twig without disturbing the bird



A prime number is a whole number, greater than 1, that is divisible only by itself and 1. Some examples of prime numbers are 2, 3, 5, 7, 11, and 13. What is the largest prime number, P, such that 9 times P is less than 400


The numbers M and N are different numbers selected from the first twenty-five counting numbers:
1, 2, 3, 4, ... , 24, 25. If M is larger than N, what is the smallest value that the expression at the right can have

M x N
_______
M - N



A printer has to number the pages of a book from I to 150. Suppose the printer uses a separate piece of type for each digit in each number. How many pieces of type will the printer have to use


A jar contains a large number of pennies. The pennies can be divided into equal shares among 3, 4, 5, 6, 7, or 8 children with no pennies left over each time. What is the least number of pennies the jar could contain

[size=8]PRIME
43

M & N
25/24

PRINTER
9*1 + 90*2 + 51*3 = 342

PENNIES
8*7*5*3 = 840

CLASSICS
1 - no smoke
2 - T (it)
3 - and?
4 - have someone else hold the nail?
5 - ?
6 - man
7 - queue
8 - uproot the whole tree?[/size]

1. Think fast: Doh! Its an electric train
2. Second most common letter--t Etaoin Shrdlu if I remember right is the order of the most commonly used letters.
3. most used word ---the
4. 3 letter word has the most definitions-run
5. How to avoid hitting your fingers, hit the head of the nail not the nail of the fingers.
6. Why did the bubble gum cross the road? It was being chewed by the chicken
7. 4 legs, 2 legs, and 3 legs- An infant, grown, and aged hairless monkey
8. Queue
9. Hold the twig the bird lands on.
10. 400/9=44.4444. 44 is not prime, but 43 is, and 9*43=387
11. M=25 and N<M=25 so N=24 and M*N=600-599=1
12. 10 +5+10=25
13. pennies 840

Rap

As you may know I don't post answers for 24 hours, in order to give those on the ?'Dark Side' a small chance. However, as I have enjoyed your answers so much, I could not resist wondering what you will make of these. All answers are logical.





9. When is a yellow dog most likely to enter a house

10.What has a head like a cat, feet like a cat, a tail like a cat, but isn't a cat

11. When is a doctor most annoyed

12.Why isn't your nose twelve inches long

13. What has five eyes, but cannot see

14, What is it that by losing an eye has nothing left but a nose

15. What has a foot on each end and one in the middle

16. Which US President had the largest shoes

9. when it sees a stranger?

11. when you stick your tongue out?

12. because then it would be a foot

14. noise

15. a yard

have to think about the others

9. When elected to congress.

10. When it's a lion (lying).

13. A potato(e)

Rap

11. When he loses his patients (patience).

Pretty Big Feet

Look at the size of dem dogs

Rap

Mark:

PRIME
43

M & N
25/24

Dare I say, : N=1, M=25


PRINTER
9*1 + 90*2 + 51*3 = 342

PENNIES
8*7*5*3 = 840



I give the stock answers, although many above are far, far better. It is interesting to see how riddles evolve and I bet many of your answers become the new ?'point of reference'.

1. An electric train would not have smoke.
2. The letter T
3. RUN
4. Hold the hammer with both hands.
5. It was stuck on the bottom of the chicken's foot.
6. A man - crawls as a baby, then walks on 2 feet, then uses a cane (3 legs) as an old man.
7. QUEUE, remove "UEUE", say Q. Q and queue are pronounced the same.
8.Wait until the bird flies away.
9. When the door is opened.
10.A kitten
11. When he is out of "patients".
12. Because it would then be a foot.
13. The Mississippi River
14. The word NOISE
15. A yardstick
16. The president with the largest feet.




Suppose the counting numbers from 1 through 100 are written on paper. What is the total number of 3's and 8's that will appear on the paper



Many whole numbers between 10 and 1,000 have 2 or 7 as the units digit. How many such numbers are there between 10 and 1,000



2, 3, 5, 7, 11, ... are examples of prime numbers; each number has only itself and I as factors. Suppose the number of units in each of the length and width of a rectangle are prime numbers and the perimeter is 36 units. What is the largest number of square units the area could have



A bus was rented at a fixed cost by a group of 30 people. When 10 people were added to the group, the fixed cost of the bus did not change, but the charge for each person in the original group was $2 less than before. If each person paid the same charge as each of the others, can you tell me the fixed cost of renting the bus

Suppose 3! means 3x2xl, 4! means 4x3x2xl, 5! means 5x4x3x2xl, and so forth. What is the value of the expression below in simplest form

8! - 6!
_____
3! X 5!

3's & 8's
40


2.3.5.7.11
11*7=77


the bus
240

2 OR 7
198

FACTORIALS
55

Usamashaker, good to see you back buddy. Do you have some good news? Have you passed your medical exams?



In response to public demand, ten more rather annoying riddles.
Do not attempt if under medication, especially the little green/yellow ones.

1. Some months have thirty days and some months have thirty-one days. How many months have twenty-eight days

2. At the hardware store I was quoted 12 cents for one, 24 cents for 50, and 36 cents for 144. I wanted six. What was I buying and how much did it cost me

3. If two boys and a girl can beat their father in a tug-of-war, but their mother can win against a boy and two girls, who should win a contest between the father and a girl against the other and a boy

4. If a crab and a half weigh a pound and a half, but the half crab weights half as much again as the whole crab, what do half the whole crab and the whole of the half crab weigh

5. A chessboard has squares that are two inches by two inches by two inches. What is the diameter of the largest circle that can be drawn on the board in such a way that the circle's circumference is entirely on black squares

6. Compose a grammatical and sensible sentence in which all words begin with the same sound and yet none begin with the same letter

7. Now compose a grammatical and sensible sentence in which all words begin with the same letter and yet none begin with the same sound

8. I started 2 watches at the same time, It turned out that one of them went two minutes per hour too slow, and the other went one minute per hour too fast. When I looked at them again, the faster one was exactly one hour ahead of the other. How long had the watches been running

9. What is so unusual about the number 2520

10. My first wears my second; my third might be what my first would acquire if he went to sea. Put together my one, two, three, and the belle of New York is the girl for me. What one word am I