The worlds first riddle!

[size=7]1) She's on foot
2) lay one board across an exterior corner. The second from the middle of the first board to the opposite interior corner
3) 20 9's
4) Uncle--the rest have an even number of letters
5) The speed of light--to average 60mph fo 2 miles takes 2 min. To climb a 1 mile hill at 30 mph takes 2 min. Consequently the driver must be at the top and bottom of the hill simultaneously. This can only happen if the car goes down the hill at the speed of light.[/size]

Rap

Suppose that you have a lot of wooden cubes. You decide to decorate them by painting the faces of each cube. You have only two colors of paint, red and blue. Each cube has 6 square faces, and you will paint each face one of these two colors (but a cube may end up with both some red faces and some blue faces).

You want to come up with a collection of cubes that are all painted differently. Here, of course, we consider two cubes to be painted the same if one cube can be rotated to look exactly like the other.

The question is this: how many different cubes can you design using only these two colors

[size=7]WOMAN
she was walking

MOAT
Place one diagonally across a corner and the other from the middle of the first to the other side.

NINES
There's only one "nine." However there are 20 nines in the numbers from 1-100.

RELATIVES
cousin - it doesn't convey a gender

HILL
infinitely fast[/size]

[size=7]CUBES
10
red/blue
6/0: 1
5/1: 1
4/2: 2 (2 opposite or adjacent)
3/3: 2 (2 opposite with a connector or all adjacent)
2/4: 2 (2 opposite or adjacent)
1/5: 1
0/6: 1[/size]

Dadpad:

woman with no drivers licence was walking

Moat... Use the drawbridge?

20 (9, 19, 29.)

Family tree......... sister (she has red hair, all the others are blonde)

average speed 120 mph

When are you guys going to drag yourselves into line with the rest of the world and go metric (Kilometres)

I will light a candle for you.

When you have 100 seconds in a minute, 100 minutes per hour, 20 hours a day, 5 day week, 5 week month, 10 month year. In addition, a tide every 5 hours. And 4X in 5 packs. :wink:

Ps. How is the backpacker murder trial going?


Rap:

1) She's on foot

2) lay one board across an exterior corner. The second from the middle of the first board to the opposite interior corner

3) 20 9's

4) Uncle--the rest have an even number of letters

That's a good one.
-or-
Uncle; it's the only one not ending in a vowel.
-or-
Cousin; it's the only one not gender specific.


5) The speed of light--to average 60mph fo 2 miles takes 2 min. To climb a 1 mile hill at 30 mph takes 2 min. Consequently the driver must be at the top and bottom of the hill simultaneously. This can only happen if the car goes down the hill at the speed of light.

(Take that you Metric martyr )




Mark:

WOMAN
she was walking

MOAT
Place one diagonally across a corner and the other from the middle of the first to the other side.

NINES
There's only one "nine." However there are 20 nines in the numbers from 1-100.

RELATIVES
cousin - it doesn't convey a gender

HILL
infinitely fast

(Inches Rule - yeah!)


CUBES
10
red/blue
6/0: 1
5/1: 1
4/2: 2 (2 opposite or adjacent)
3/3: 2 (2 opposite with a connector or all adjacent)
2/4: 2 (2 opposite or adjacent)
1/5: 1
0/6: 1



Damn! Oh, I mean, well done.

There are 10 different ways to color the cubes. They can be counted as follows:
• one cube is all red
• one cube is all blue
• one cube has 5 red sides and one blue side
• one cube has 5 blue sides and one red side
• two cubes have 4 red sides and 2 blue sides (you can put the two blue sides either across from each other or next to each other)
• two cubes have 4 blue sides and 2 red sides (similar reasoning)
• two cubes have 3 red sides and 3 blue sides (either two red sides are across from each other or all the red sides surround some corner of the cube).







There are a lot of interesting math problems that can be built around finding probabilities. Suppose we are doing a random experiment (such as tossing a coin or throwing a die) where all outcomes are equally likely. We can turn the experiment into a game by deciding which outcomes will be "wins" and which outcomes will be "losses".

(For example, we might decide that we will "win" a dice throwing game if the number on the die turns out to be 1 or 5. The outcomes 2, 3, 4, and 6 will mean we "lose" the game.) The probability of winning is then just a simple fraction:

[the number of "winning" outcomes] OVER [the total number of all outcomes]

(So in our simple dice throwing game, there is a probability of 2/6 we will win, since there are two winning outcomes and 6 total outcomes.)


Now here is a harder task. A bin contains 25 balls: 10 red, 8 yellow, and 7 blue. We draw three balls at random (without looking!) from the bin, and we will say that we "win" if our three balls represent exactly two colors.
(That is, we "win" if we draw two balls of one color and another ball of a different color.)

What is the probability of winning this particular game



Eight men wanted separate rooms in a hotel, but there were only seven rooms available. The clerk said he could handle it and proceeded to put two men in the first room, the third man in the second room, the fourth man in the third room, the fifth man in the fourth room, the sixth man in the fifth room, and the seventh man in the sixth room. He now took one of the men from the first room and placed him in the last, the seventh, room. So he managed to put eight men into seven rooms with each one having a separate room.

Did he really


A three-volume set of books stands on the bookshelf. Each cover is 1/4 of an inch thick and the pages of each book are one inch thick. A bookworm starts on page one of volume one and eats his way through to the last page of volume three.

How far does he travel



A secretary types four letters to four different people and addresses four envelopes. She puts the letters into the envelopes at random without looking. What are the chances that exactly three will be in the correct envelopes


A brick weighs 4/5 of its weight plus 4/5 of a pound. How much does the brick weigh

[size=7]PROBABILITY GAME
1529/2300

EIGHT MEN
He never put the eighth man in a room.

BOOKWORM
2 inches

ENVELOPES
0

BRICK
4 pounds[/size]

If you take a markr and start from a corner on a cube, what is the maximum number of edges you can trace across if you never trace across the same edge twice, never remove the markr from the cube, & never trace anywhere on the cube, except for the corners and edges



At Probability University, there are 375 freshmen, 293 sophomores, 187 juniors, & 126 seniors. One student will randomly be chosen to receive an award.

What percent chance is there that it will be a junior
(Round to the nearest whole percent.) :wink:

[size=7]8 & 19%[/size]

Rap

[size=7]CUBE
9
There are eight vertices all with odd degree. Therefore, four separate 'lines' will have to be drawn. Minimizing three of them to an edge each leaves a maximum of nine edges for one line. Trace one face (4), trace an edge to the opposite face (1), and trace that face (4).

PROBABILITY U
19%[/size]

Rap:
Probability University.
19%

On reflection, that may have been on the easy side for A list clebs.
However, I take some comfort from the fact that it was too difficult for Australians, Canadians and the French.


19%. Divide the number of juniors (187) by the total number of students (981), & then multiply the number by 100 to convert to a percentage.


Mark:

PROBABILITY GAME
1529/2300 /


Nice one Mark, oh and five, two etc.


The probability of winning is 1529/2300. Here's an analysis that gets you to that answer.

We first need to count the number of possible outcomes there are to our game of drawing 3 balls from the bin. Recall that the number of ways to choose k objects from a set of n objects is C(n,k) = n! / [k!(n-k)!]. In our case, we are choosing 3 balls from a set of 25 balls, so the number of choices is
C(25,3) = 25! / [3!22!] = [25*24*23] / [3*2] = 2300

Now we just need to figure out how many of those possible choices will win the game. In order to win we need to do one of three things: (1) draw exactly 2 red balls (with the third ball being some other color), (2) draw exactly 2 yellow balls, or (3) draw exactly 2 blue balls.
To choose exactly two red balls amounts to choosing two balls from the set of 10 red balls, followed by picking any of the 15 non-red balls as the third choice. So, the number of ways to choose exactly 2 red balls is
C(10,2)*15 = 45*15 = 675 .
Similarly, the number of ways to choose exactly 2 yellow balls is
C(8,2)*17 = 28*17 = 476
and the number of ways to choose exactly 2 blue balls is
C(7,2)*18 = 21*18 = 378 .
So, the total number of winning choices is
675+476+378 = 1529 .
So, the probability of winning this game is 1529/2300 .


EIGHT MEN
He never put the eighth man in a room.

BOOKWORM
2 inches

(I have: Four inches. He doesn't eat the front cover of volume one nor the back cover of volume three)



ENVELOPES
0

BRICK
4 pounds

1/5 of the bricks weight = 4/5 of a pound
4/5 of a pound x 5 = 4 pounds
(Multiplying by 5 is the same a dividing by 1/5)



PROBABILITY U
19%

CUBE
9
There are eight vertices all with odd degree. Therefore, four separate 'lines' will have to be drawn. Minimizing three of them to an edge each leaves a maximum of nine edges for one line. Trace one face (4), trace an edge to the opposite face (1), and trace that face (4).

To verify this, you can make a drawing of a cube, & number each of its 12 edges. Then, always starting from 1 corner & 1 edge, you can determine all of the possible paths for tracing along the edges of a cube. There is no need to start from other corners or edges of the cube, as you will only be repeating the same paths. The process is a little more involved than this, but is useful for solving many types of spatial and logical puzzles.


Talking of cubes:

A cube is made of a white material, but the exterior is painted black. If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have 2 of their sides painted black



A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now her salary is $22702.68. What was her salary to begin with



Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 miles/hour. What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide, assuming that neither train changes its speed prior to collision

The trains are on the same track headed in opposite directions (i.e. directly toward one another).

"(I have: Four inches. He doesn't eat the front cover of volume one nor the back cover of volume three)"

He only eats the front cover of volume one, all of volume two, and the back cover of volume three.

Yes, that makes more sense. I was measuring in hectometres

Another day, another set of trials and errors.



If the same functions are applied to reach the results in each of the three sets of numbers, find what number should replace the in the last set:





You have 1,432 feet of fence that must be strung out in a straight line. A fence post must be placed for every 4 feet of fence, so how many fence posts will be needed



If each letter in the following equations represents a number from 1 through 9, determine what number each letter represents
(Three possibilities).

1. A+A+B+C = 13

2. A+B+C+D = 14

3. B+B+C+D = 13

[size=7]FENCE
359

LETTERS
A, B, C, D
2, 1, 8, 3
3, 2, 5, 4
4, 3, 2, 5[/size]

[size=7]FUNCTIONS
60

A B
.C
D E

C = |A-D| * (|B-E| + 4])[/size]

Mark:
(A man of …)

LETTERS
A, B, C, D
2, 1, 8, 3
3, 2, 5, 4
4, 3, 2, 5



FUNCTIONS
60 (although that works)

A B
.C
D E

C = |A-D| * (|B-E| + 4])



30 - In each set, the difference between the two leftmost numbers is divided by two, and then multiplied by the sum of the two rightmost numbers. The product is written in the middle for each set.

I would suspect there are a number of variations on this theme.


FENCE
359





Halloween Weekend - wooOoo



The Par family had several guests for a Halloween weekend. The menu for dinner included turkey and candied yams (of course!) as well as orange rolls and pie. There was a lot of leftover food (except for the yams -- they disappeared quickly), making for good snacking all weekend. Each of the pies had been cut into six pieces, giving a total number of pie slices equal to the number of orange rolls initially baked by Mrs. Par.

At dinner on Thursday everyone ate two orange rolls and one slice of pie each. That night four of the guests left for home, but the next day everyone remaining at the house ate another orange roll and three more slices of pie each. As of Friday night, Mr. Par noted that there were still 7 orange rolls and two-thirds of a pie remaining.

Turkey sandwiches were also very popular fare that weekend. On Friday everyone in the house ate an equal number of turkey sandwiches. Two more guests left for home on Friday night. Then on Saturday everyone remaining at the house ate an equal number of turkey sandwiches, though they ate one fewer sandwich per person than they had eaten on Friday. Mr. Par calculated that there were eleven more sandwiches eaten on Friday than were eaten on Saturday.

Now, sort through all of that and tell me: how many turkey sandwiches were eaten at the Par house on Friday



At a Halloween dinner for five people, two identical serving bowls of candied yams are passed around the table. The first two people take their servings from the first bowl, and each of them takes the same amount, say X % of the total in the bowl. The other three people take their servings from the second bowl and don't take equal amounts. However, each of these three people takes X % of what remains in the bowl when it is passed to them.

After the five people have taken their servings, the two bowls have equal amounts left in them.

Now here's the question: if each bowl initially contained one pound of candied yams, how much remains in each bowl after the servings are completed

[size=7]YAMS
23.6%[/size]

[size=7]TURKEY SANDWICHES
21
There were 36 rolls and 6 pies and 11 people at the start.[/size]

Mark, you are a genius. Single handed you continue to unravel the worlds mysteries. Kudos partner.

TURKEY SANDWICHES
21
There were 36 rolls and 6 pies and 11 people at the start.

YAMS
23.6%



Here's a spooky problem to ponder --- if you dare!

The ghoulish inhabitants of a ghost town decide to build themselves a new home -- that is, a brand new cemetery. They have scraped together $10,000 (by selling their gold fillings and haunting their rich living relatives).

They plan to use as much of the vacant land north of Creepy Street as they need, but they will need to build a rectangular fence around the new cemetery. On the three sides of the rectangle not facing Creepy Street they will use materials costing $10 per foot of fence. But on the one side which borders Creepy Street, they need more expensive materials costing $15 per foot.

In order to make their new home as large as possible in area, what dimensions should they choose for the rectangular cemetery

Remember, they have $10,000 to spend on the fence.




Anyone telesent (like being teleported or "beamed up") to Space Station Exray will arrive in pod A, B, or C. You are twice as likely to arrive in pod A than in pod B, & three times as likely to arrive in pod B than pod C.

How likely is it that you will arrive in pods B, C, & A, in that order, the only three times that you are telesent to Space Station Exray

Please express any answer either as a fraction, or a percentage if you prefer.

[size=7]FENCE
200x250 (with the 200 bordering Creepy Street)

PODS
1.8%[/size]