The worlds first riddle!

Mark:

two solutions:

__K
QJQ
_AKJ
__A

__K
QJQ
_AKA
__J


That is remarkable, I only had the first one, it never occurred to me that there might be another way.




Which is worth more: A pound of $10 gold pieces, or half a pound of $20 gold pieces

Let's assume that a $20 gold piece weighs twice as much as a $10 gold piece.

a) So, which would you rather have, a half pound of $20 gold pieces or a pound of $10 gold pieces?

b) You think I must be barking mad because there is no difference.

[size=8]Since the value is proportional to the weight, a pound is worth twice as much as half a pound.[/size]

A car travles at 60 miles per hour for sixty minutes. The car makes the return trip over the exact same distance at 30 miles per hour. What is the average speed of the car

60 miles in 1 hour out
60 miles in 2 hour back

for a total of 120 miles in 3 hours, so average speed is 40 mph..

Ok! Enough of this easy stuff, lets kick it up a notch and get down and dirty:


I have a square piece of wood which measures 2 feet on each side.
If it is cut into a regular octagon (8 sided figure, all sides and angles equal), what does each of the 8 sides measure

Oh come on we can be harder than that...

if X is segment length, and a is vertical contribution of the angled segment, total height is:

2 = 2a + X

By pyth-thm,
sqrt(2a^2) = x

Therefore a = x/sqrt(2)

plugging in,

2(x/sqrt(2)) + x = 2

solving,

(sqrt(2) + 1)x = 2

Rearranging,

x = 2/(sqrt(2)+1) = 0.828...

Next question:

You have a bunch of sticks of random lengths (all different) and you want to use them to construct the best circle you can. Given a stick of length N, at what angle should you place this stick from the previous stick in order to best fit it to a circle of radius R?

Wouldn't that depend, at a minimum, on the length of the previous stick?

Do you have to use all of the sticks, or can you use an optimal subset?
Can you choose R?

How are you defining best fit? Is it a continuous version of least squares?

You're right, that was ambiguous.

With each stick, you want the endpoint to intersect the circle. This doesn't depend on the previous stick if you define the rotation from the standard coordinate system. You do not choose the sticks, just pick them one at a time out of a bag and have to use each one you get.

So you end up with an inscribed polygon, correct?

The angle between two chords that share a common point on the circle depends on the lengths of both chords.

Perhaps I don't understand, but aren't you asking for the angle between adjacent sides (chords)?

Perhaps the circumference of a circle of radius "r" is given by the formula 2*Pi*r
A unit of plane angle measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Which I make: 57.295 degrees

inscribed polygon in a circle yes. I did initially ask for the angle between sides but if you define the angle in terms of the standard coordinate system instead, it can be a function of only N and R.

I'm still confused. We need two line segments to form an angle. Is one endpoint of the stick at (R,0), and are you then asking for the angle between the stick and the X-axis?

Yes

acos(N/2R)

Doesn't look right to me. How do you figure?

Let the circle of radius R be centered at the origin.
Let the endpoints of the stick be A=(R,0) and B (a point on the circle).
Let C be the point (-R,0).
Angle ABC is right since AC is a diameter.
cos(CAB) = AB/AC = N/(2R)
angle CAB = acos(N/(2R))

I should have grouped the 2R in my previous post to make my intentions clear.

What did you get?

Mark:

Since the value is proportional to the weight, a pound is worth twice as much as half a pound.


At first glance this seems to be similar to that old puzzle - "what's heavier - a pound of feathers or a pound of lead?" And the answer is they are the same thing.
However, this is a twist on that old puzzle. Let's suppose (to keep things simple) that a $10 gold piece weighs an ounce and a $20 gold piece weighs 2 ounces. So a half pound (8 ounces) of $20 gold pieces is 4 coins equalling $80. A pound (16 ounces) of $10 gold pieces is 16 coins totalling $160.
Basically, this puzzle is asking, "would you rather have a half pound of gold or a pound of gold?"

Which is what Mark said in 19 words.



Stu:


60 miles in 1 hour out
60 miles in 2 hour back

for a total of 120 miles in 3 hours, so average speed is 40 mph.


I could not have put it better, so I won't.

I then brought the eight sided square outta the old kitbag, to which Stu replied…

Stu:
if X is segment length, and a is vertical contribution of the angled segment, total height is:

2 = 2a + X

By pyth-thm,
sqrt(2a^2) = x

Therefore a = x/sqrt(2)

plugging in,

2(x/sqrt(2)) + x = 2

solving,

(sqrt(2) + 1)x = 2

Rearranging,

x = 2/(sqrt(2)+1) = 0.828...


For those of you that don't understand all the Maff stuff:

Using Geometry:
Construct a square in the 'upper left' side of the square. Each of the sides of this square would be 1 foot because the piece of wood is 2 feet square. Using the Pythagorean Theorem, the diagonal of this smaller square would be the square root of 2 or 1.414213562. Now if we draw a line at the upper left to represent one of the sides of the octagon, it would 'slice' the diagonal at precisely the 1 foot mark with the remaining segment of the diagonal equal to .414213562 feet.
This segment is precisely one half the length of 1 of the sides of the octagon because it is part of a 90-45-45 triangle. Therefore, each of the octagon's sides would equal .828427124 feet or 9.941125497 inches.


Using Trigonometry:
From the center of the square, draw a perpendicular bisector to one of the sides of the octagon. The height of this bisector is 1 foot. Since each side of the octagon subtends a 45 degree angle with the center, then the angle subtended by the perpendicular bisector and a line to the end of 1 side would be 22.5 degrees. The 'half-side' length would equal tan 22.5 degrees times 1 foot which equals .414213562 feet and the full-side length is double this or .828427124 feet or 9.941125497 inches.


Stu, may I enquire; Do you is, or do you don't gotta answer for your very good question?


Whilst waiting for a reply…

If a chicken and a half can lay an egg and a half in a week and a half, how many eggs would one chicken lay in a month and a half (6 weeks)



Yeah, yeah, I hear you sigh, the Chicken question is a no brainer, well…


Twelve is the smallest positive integer that can be divided by the integers 1, 2, 3 and 4 with no remainder. What is the smallest positive integer that can be divided by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 without any remainder

[size=8]CHICKEN
1 egg per chicken each 1.5 weeks.
4 eggs in 6 weeks

NO REMAINDER
2^3 * 3^2 * 5 * 7 = 2520[/size]

An employee is to be rewarded with a $250 bonus AFTER TAXES have been deducted. If the federal tax is 15%, the state tax is 10% and the Social Security is7.5 %.

What must the GROSS PAY be in order for the net pay to be $250