The worlds first riddle!

Divisibility:2519
dividing by 2, 5 and 10 - # must end in 9
dividing by 3 and 9 - must be of form 89+90n
dividing by 8 and 4 - must be of the form 39+40m
from above - must be of form 359+360p (dividing by 6 already in)
dividing by 7 - must be of the form 69+70q; p=6 q=35 yields 2519 h
mm patterns... 'must be of the form [x + (x+1)y]'....just 1 shy of 2520 which is divisible by all integers 2-10

[size=8]RUMOR
5,726,623,061 people will know after 8 hours.

SMALLEST NUMBER
2519
10!-1 is the obvious answer, but there are extra factors that can be removed from 10!.[/size]

Thoh:

Rumor: 8 hrs.
1 + 4 + 4^2 + 4^3 + 4^4 + ... + 4^n = 5.6 x 10^9
the sum is approximately 4^n / (1-1/4) = 5.6 x 10^9
solving for n, n = 15.98 ~ 16
every even power of 4 takes 1 hr so 16/(1hr/30min)=16/2=8hrs

Mark:

RUMOR
5,726,623,061 people will know after 8 hours.


Do you find it as amazing as I do that the whole world could be informed in as little as eight hours?


Thoh:

Divisibility:2519
dividing by 2, 5 and 10 - # must end in 9
dividing by 3 and 9 - must be of form 89+90n
dividing by 8 and 4 - must be of the form 39+40m
from above - must be of form 359+360p (dividing by 6 already in)
dividing by 7 - must be of the form 69+70q; p=6 q=35 yields 2519 h
mm patterns... 'must be of the form [x + (x+1)y]'....just 1 shy of 2520 which is divisible by all integers 2-10

Mark:

SMALLEST NUMBER
2519
10!-1 is the obvious answer, but there are extra factors that can be removed from 10!.

Great answers guys!



Ok, I am really excited about this one, it's baffling simplicity belies it's cunning complexity, because; each of the top three rows of numbers demonstrates the same arithmetical pattern. When, I mean if you discover what the pattern is, what number should be substituted for the question mark.

7 4 8
3 9 7
6 5 10
8 4

How about 3?

I'll explain my reasoning if it's correct.

Three! 3 you say!
What three letter word best completes the below words

...EW
B...ET
C...ET
M...

3 letter word: ask

askew
basket
casket
mask

Mark:

How about 3?


By an amazing coincidence, the answer is 3.

7 x 4 - 8 = 20
3 x 9 - 7 = 20
6 x 5 - 10 = 20
3 x 8 - 4 = 20

Is that how you saw it, or is there another way?


Stormy:
3 letter word: ask

askew
basket
casket
mask

Congrats, it looks so easy when you see the answer, before that it looks impossible.



The old cog railway at Storm Peak leaves the station at Bed Springs, at an altitude of 6,571 feet and climbs to an altitude of 14,110 feet at its summit.

For those of an inquisitive nature, assume the average grade is 16 percent.

What I ask; is the total length of the track from the station to the summit

And if you have any idea of the angle of elevation



For those who do not have a head for heights: Which word in the English language becomes shorter when it is lengthened

word:short

AMAZING COINCIDENCE
That's how I saw it.

[size=8]TRAIN TRACK
angle of elevation = atan(.16) = 9.09 degrees
length of track = (14110-6571) / sin(9.09) = 47718 feet = 9 miles[/size]

Thoh:
word: short


Mark:

TRAIN TRACK
angle of elevation = atan(.16) = 9.09 degrees
length of track = (14110-6571) / sin(9.09) = 47718 feet = 9 miles


I have run outta superlatives to espouse your answers.

Since the vertical gain is 7,539 feet (found by subtracting 6,571 from 14,110), you can find the horizontal distance (if it were thought of as a right triangle) by dividing .16 into it. So the horizontal change is 47,118 feet. Then using the Pythagorean Theorem, the total amount of track would be 47,718 feet or 9.03 miles. The angle of elevation is found by taking the inverse tangent of 0.16, which is 9.09 degrees.




Some believe it was Benjamin Franklin who said, "Compound interest is the eighth wonder of the world," while attributing "Compound interest is the world's greatest discovery," to Albert Einstein. Still, drunken Joe attributes the whole thing to Try A. Gain. Whoever said it first; at least two great minds recognized the power of compounding.

So let's take two twins; Benjamin and Albert who graduate from high school at age 18. Ben, an industrious type, works an extra job delivering pizza and puts $2000 on the first of each year into an IRA. Al, meanwhile, works on his Ph.D. and spends his meager stipend on Pizza and Root Beer at State U. Ten years later, Ben is busy running his print shop, has a family and decides he can't contribute to his IRA any more, so he stops contributing. Meanwhile, Al at 28, has graduated, and has landed a new teaching job and starts putting his $2000 a year into his new IRA.

Forty years later at the age of 68, both are ready to retire. Ben has contributed $20,000 to his IRA (during the first ten years). Al has contributed $80,000 to his IRA (during the last forty years), four times as much.

Assuming both Ben and Al earn 8% every year compounded annually (figured on the last day of the year), how much does each have for their retirement


I know a word of letters three. Add two, and fewer there will be. What word do I be

[size=8]WORD
few[/size]

Yeah, I know Christmas is coming, but I simply must stop giving the answer in the question.


Suppose you have an open topped box that is 5 cm x 5cm x 5 cm. Inside the box is a steel ball bearing that is 25 cubic centimetres. Next to the box is a two litre pail filled with mercury.

How many cubic centimetres of mercury would you have to pour into the box to completely submerge the ball bearing

you can't submerge the bearing because it will float on top of the mercury

[size=8]AL AND BEN
Ben has $679,781.46
Al has $559,562.08[/size]

[size=8]STEEL BALL
Found this on the web:

"The relative density of steel is 7.7 and that of mercury is 13.6."

Notice the lack of units. This supports thoh13's assertion.[/size]

This problem is sponsored by Toys are bust:

There is a very long baby gate, which is advertised as being able to be used as a play yard for children ("A gate that doesn't quit"). This 6-panel play yard "provides 18-1/2 square feet of protected play area when it is set up as a hexagon." The ad continues by saying that the play area expands to so many square feet simply by adding a 2-panel expansion kit.

Assuming that all the panels are the same width, what is the width of each panel

Also, ( yes, there is more to come) determine how many square feet of space would be provided by the octagon (by adding the 2-panel expansion kit to the hexagon)



If you were to step into a sealed room filled with 100% methane gas and strike a match, what would happen

[size=8]BABY GATE
panel width = 2.669 feet
area of octagon = 34.382 square feet (almost double)

METHANE
Nothing would happen to the match, but you'd suffocate if you didn't get out soon (for the same reason that nothing happend to the match).[/size]

Mark:

BABY GATE
panel width = 2.669 feet
area of octagon = 34.382 square feet (almost double)


The advertisement never mentioned the length of each, but the ad gave 34.4 square feet as the area.

To solve the problem, you can draw three diagonals of the hexagon which intersect in the center, thus forming six equilateral triangles.
Letting x represent the side of the panel (and therefore, the length of each side of the six equilateral triangles), you can set up a formula for the area of the hexagon:

To solve for the area of the octagon, draw the four diagonals which intersect in the center of the octagon. This forms 8 isosceles triangles with angle measurements 67.5, 67.5, and 45 degrees. The side opposite the 45 degree angle is 2.668 feet (the length of the panel).

Draw an altitude from the center of the octagon to one of the eight panels. This divides the triangle into two smaller right triangles whose acute angles measure 22.5 and 67.5 degrees. The leg opposite the 22.5 degree angle is 1.334 (half the length of the panel). Call the other leg h. Use the tangent function to solve for h:

Alternatively, do it Mark's way and save yourself a heap of time.


Mark:

METHANE
Nothing would happen to the match, but you'd suffocate if you didn't get out soon (for the same reason that nothing happend to the match).




The first of seven cross country runners, each bearing a number from 1 to 7, (original eh!) crossed the tape at 12:01 and the others at intervals of 1 minute apart (no ties).

If "time" stands for the number of minutes after 12:00, determine the order in which the runners finished

(A) The highest total of runner and time (13) occurs just once.
(B) The lowest total of runner and time (4) occurs just once.
(C) The total 9 (of runner and time) occurs 3 times.
(D) Just four runners have numbers larger than their times.
(E) The winner's number exceeds that of the second place finisher.

[size=8]CROSS COUNTRY
1: 6 total = 7, N > T, 6 > 3
2: 3 total = 5, N > T
3: 1 total = 4
4: 5 total = 9, N > T
5: 4 total = 9
6: 7 total = 13, N > T
7: 2 total = 9[/size]

In a recent "Ask Marilyn" column, someone asked about a modified version of the Monty Hall problem. In the modified version, Monty doesn't know which door leads to the prize. Therefore, he's not sure which door he can open (without revealing the prize) before offering the contestant the opportunity to switch to the other unopened door. So, he guesses (correctly). The question put to Marilyn was whether or not the contestant should switch doors. In the original problem, the contestant wins with probability 2/3 if (s)he switches. Marilyn correctly noted that in the modified version, it makes no difference - the contestant will win with probability 1/2 in either case.

If there are 1000 doors and Monty guesses correctly 998 times leaving your door and one other unopened door, what is your probability of winning if you do/don't switch doors?

FYI: In the original problem (Monty knows which doors he can open), you would win with probability 999/1000 by switching.