OpenLLM-France/wikimedia huggingface dataset:
# Puzzles/Statistical puzzles/3 Bags of Marbles/Solution

Puzzles | Statistical puzzles | Puzzles/Statistical puzzles/3 Bags of Marbles | Solution
2/3, or approximately 66.7%

## Reasoning

The most common wrong answer is 50%. This is due to the misconception that you are given the information that you have picked either bag #1 or bag #3 [Challenge: This is not a misconception - This information is already provided in the question - a fact] . This is not the case, as explained below:
Label each of the marbles: bag 1 contains 1a and 1b, bag 2 contains 2a and 2b, and bag 3 contains 3a (white) and 3b (black). Because you picked a random bag and a random marble, each marble has an equal chance of being picked. Given that you picked a white marble, you have the following distribution:
First marble:
* 1a: 1/3
* 1b: 1/3
* 2a: 0 (black ball was not picked)
* 2b: 0 (black ball)
* 3a: 1/3
* 3b: 0 (black ball)
Given this information, we look at each situation:
* 1a: You have picked bag #1, so the second marble must be 1b, a white marble.
* 1b: You have picked bag #1, so the second marble must be 1a, a white marble.
* 3a: You have picked bag #3, so the second marble must be 3b, a black marble.
If you are in the first two situations, your second marble will be a white marble, therefore, adding 1/3 and 1/3, you get 2/3 chance of getting a white marble
Note: This solution is INCORRECT - see the section titled "Correct Answer" below.

## Algebraic explanation

Let W be the event of drawing a white marble, WW be the event of drawing from bag 1 (two white).
Then P(WW | W) = P(WW ∧ W) / P(W) = P(WW) / P(W) = (1/3) / (1/2) = 2/3.
Note: This is an algabraic representation of the INCORRECT solution above. Please see the "Correct Answer" section below.

## Correct answer

Correct answer - 50% - is commonly considered wrong, but really - past events have no influence on future probabilities at all (You cannot count "You have picked bag #1" twice. You just either did it or not). Right now You have one white marble in your hand and knowledge, that another one is either black or white depending on which bag (out of two) you selected.
Challenge: You essentially just start by picking a marble--and there are three white marbles. Two of those white marbles are in the same bag as another white marble; so, given that you've picked one of the three white marbles, 2/3 of the time its pair matches--right?
Rebuttal: You're thinking about this wrong - since you picked a white marble, you know you have chosen from either bag #1 or bag #3. Now, there are only two possible outcomes - either you have bag #1, in which case the other marble is white, or bag #3 in which case it's black. And the probability is 50% that the other marble in your chosen bag is white.
# Puzzles/Statistical puzzles/A Bug Running/Solution

Puzzles | Statistical puzzles | A Bug Running | Solution
The bug must move seven times to the right and seven times up. Any such sequence, e.g. RRUUURURRUURUR is a valid path. Therefore the solution is ${14 \choose 7}=3432$. In the case of an $n$ x $n$ board the answer is ${2n-2 \choose n-1}$.
# Puzzles/Statistical puzzles/Summing n/Solution

The solution is easily found if the problem is restated graphically. Consider n=3, k=2. Possible sums are 3 = 0+3, 3 = 1 + 2. A graphical representation could be:
, respectively, with the bars representing separations between the summands and 'o's representing the value of the summands. Then obviously the problems is equivalent to finding the number of ways to distribute $k-1$ bars among $n+k-1$ slots, since we need only $k-1$ bars to partition the space into $k$ summands. Therefore the solution is $N={n+k-1 \choose k-1}$, if $N$ denotes the number of unique sums.
For the next part, set aside $k$ 'o's since each partition has to have at least $1$ 'o'. Now the problem reduces to the previous one with a reduced value of $n$ i.e. $n-k$. So the solution is
$N={n-k+k-1 \choose k-1}={n-1 \choose k-1}$,
if $N$ denotes the number of unique sums.
# Puzzles/Statistical puzzles/The Pentagon

Puzzles | Statistical puzzles | The Pentagon
You are standing near The Pentagon. Given you are standing far enough away that you are not only seeing one side, what is the probability of you seeing only two sides?
Solution
# Puzzles/Statistical puzzles/A Bug Running

Puzzles | Statistical puzzles | A bug running
Consider a chess board of dimension $8\times 8$:
* A bug sits in the lower left corner and intends to reach the upper right corner, where food is present ready to be consumed. Given that the bug can only move either right or up, how many possible unique paths lead to the food?
* Given the board is $n\times n$, how many paths do exist?
* Given the board is three dimensional $n\times n\times n$, bug and food in opposite corners and movements are steps in positive directions in either dimension, how many paths do exist?
* Given the board is $k$ dimensional $n^{k}$, bug and food in opposite corners and movements are steps in positive directions in either dimension, how many paths do exist?
Consider again the $8\times 8$ setting.
Solution
# Puzzles/Stripe

Stripe are type of puzzles which stripes (lines) had to be drawn in order to complete the puzzle.

## Fences
### Rules

* Join all dots (without exceptions) to form a single loop
* The loop cannot cross or touch itself at any points
* Only horizontal and vertical lines between dots are allowed
* Some parts of the loop are already given
* Examples of Fence puzzles
* Bold lines indicates the connected lines made

## Bridges / Hashiwokakero
### Rules

* Join circled numbers with horizontal or vertical lines
* Each number must have as many lines connected to it as specified by its value
* No more than 2 lines may join any pair of numbers and no line may cross
* The finished layout must connect all numbers, so that you can travel between any pair of numbers by following one or more lines
* Examples of bridge puzzle
* Examples of solved bridge puzzle

## Walls
### Rules

* Draw a single horizontal or vertical lines across full width or the height of the center of every white cell
* The total length of all lines touching each black cells must be equal to the number printed on the cell. The length of a line is the number of cells it cover
* Examples of wall puzzle
* Example of solved Wall puzzle

## Slitherlink
### Rules

* Draw a single loop by connecting together some dots so that each numbered square has the specified number of adjacent line segment
* Dots can only be joined by horizontal or vertical lines
* The loop cannot touch , cross or overlap itself in any way.
* Empty slitherlink puzzles
* Solved Slitherlink Puzzles

## Number link
### Rules

* Draw a series of separate path, each connecting a pair of identical numbers
* No more than one line can enter any cell, and line can travel horizontally, or vertically between cells.
* Example of number link puzzles
* Examples of solved number link puzzles

## Yajilin
### Rules

* Draw a single loop by joining empty cells with horizontal and vertical lines, such that the loop do not revisit any cell.
* Any empty cells which the loop does not visit must be shaded. Shaded cells cannot touch except diagonally
* Arrows in cells indicate exact number of shaded cells in given direction
* Not all of shaded cells are identified by arrows

## Masyu
### Rules

* Draw a single loop using only horizontal and vertical lines that passes through center of each every circle
* White circle - Pass thru in a straight line
* Black circle - 90 degrees turn
* If the loop hit the wall, need to turn 90 degrees
* The loop cannot enter any cells more than once
* Examples of Masyu solved puzzles
# Physics Study Guide/Periodic Motion
## Springs
### Hooke's law

$k$ is the spring constant and $x$ is the displacement (the force is the restoring force)
For this equation to be approximately accurate, $x$ needs to be below the spring's elastic limit. If $x$ is more than the spring's elastic limit, the spring will exhibit "plastic behaviour" meaning that it will not return to its original position.

### Potential energy

potential energy stored in a compressed recoiled spring
$T$ is the period, $m$ is the mass, and $k$ is the spring constant.
# DESCRIPTION:

Verifies if the DSA signature of a binary is correct
DSA-VERIFY-SIGNATURE is a native value.

# ARGUMENTS

* obj -- The DSA key object (Type: object)
* data -- Data to which the signature applies (Type: binary)
* signature -- Signature to check (Type: object)
# Rebol Programming/dtw-keymap

DTW-KEYMAP is a block of value:
# DESCRIPTION:

Print face info for entire pane. (for debugging)
DUMP-PANE is a function value.

# ARGUMENTS

* face -- (Type: object)
# DESCRIPTION:

Creates a DSA signature
DSA-MAKE-SIGNATURE is a native value.

# REFINEMENTS

* /sign
** obj -- The DSA key object (Type: object)
** data -- Data to sign (Type: binary)
# DESCRIPTION:

Copies console output to a file.
ECHO is a function value.

# ARGUMENTS

* target -- (Type: file none logic)

# (SPECIAL ATTRIBUTES)

* catch
# DESCRIPTION:

Generates a new private/public key pair
DSA-GENERATE-KEY is a native value.

# ARGUMENTS

* obj -- The DSA key object (Type: object)
# DESCRIPTION:

Creates a key object for DSA
DSA-MAKE-KEY is a native value.

# REFINEMENTS

* /generate
** length -- Key length (Type: integer)
# DESCRIPTION:

Print face info for entire pane. (for debugging)
DUMP-FACE is a function value.

# ARGUMENTS

* face -- (Type: object)
# Rebol Programming/dtw-skin

DTW-SKIN is an object of value:
# DESCRIPTION:

Returns a block of information about an object.
DUMP-OBJ is a function value.

# ARGUMENTS

* obj -- (Type: object)

# REFINEMENTS

* /match -- Include only those that match a string or datatype
** pat -- (Type: any)
# Real Estate Financing and Investing/What Are The Disadvantages With Real Estate

Real estate investing is not free from problems. Watch out for the following:
# Real Estate Financing and Investing/What Price To Pay

After you found the house you like, you must decide what price to pay for it. In most cases, there is room between the price sellers ask and the price that they are willing to accept. Make sure that you are not paying more for a property than its market value. To determine the maximum price to pay for the property is not an easy task. Two methods are widely used in practice.
The computer should be able to give you recent history of sales in the neighborhood. The price that a subject property can bring must be adjusted upward or downward to reflect the difference between the subject property and comparables. Since this particular approach is based on selling price, not asking prices, it can give you a good idea about the market.
Appraisal is not a science, but a complex and subjective procedure that requires good information about specific properties, their selling prices, and applicable terms of financing. The use of an expert may well be worth the cost if you worry about the possibility of paying too much.
# Real Estate Financing and Investing/What Types of Real Estate Investments Are There

Kinds of real estate in which you can invest include:
* Undeveloped land
* Residential rental property (e.g., single family houses for rental, and multi unit apartments)
* Commercial property (e.g., office buildings, shopping centers, and industrial property)
* Real Estate Investment Trusts (REITs)
# Real Estate Financing and Investing/What Are Real Estate Investment Trusts

Real estate investment trusts (REITs) are corporations that operate much like closed end mutual funds, investing shareholders' money in diversified real estate or mortgage portfolios instead of stocks or bonds. Their shares trade on the major stock exchanges or over the counter.
By law, REITs must distribute 95 percent of their net earnings to shareholders, and in turn they are exempt from corporate taxes on income or gains.

## How about REIT Yields?

Since REIT earnings are not taxed before they are distributed, you get a larger percentage of the profits than with stocks. REIT yields are high, ranging between 5 1/2 to 10 1/2 percent.

## What are the Types of REITs?

There are three types of REITs: Equity REITs invest primarily in income producing properties; mortgage REITs lend funds to developers or builders; and hybrid REITs do both. Experts feel that equity REITs are the safest.

## What You Should Know about REITs

Pluses:
* Dividend income with competitive yields
* Potential appreciation in price
* A liquid investment in an illiquid area
* Means of portfolio diversification and participation in a variety of real estate with minimal cash outlay
Minuses
* Possible glut in real estate or weakening demand
* Market risk: possible decline in share price
* Safety: Low
* Liquidity: Very high: shares traded on major exchanges or over the counter and therefore sold at any time
* Taxes: Income subject to tax upon sale

## How Should You Select a REIT?

Before buying any REIT, be sure to read the latest annual report, The Value Line Investment Survey or Audit Investment`s Newsletter, Realty Stock Review. For more on REITs, visit the National Association of Real Estate Investment Trusts.
Check the following points:
* Track record: how long in business as well as solid dividend record.
* Debt level: make sure that the unsecured debt level is low.
* Cash flow: make sure that operating cash flow covers the dividend.
* Adequate diversification: beware of REITs investing in only one type of property.
* Property location: beware of geographically depressed areas.
* Type of property: nursing homes, some apartment buildings, shopping centers presently favored; "seasoned" properties preferred.
* Aggressive management: avoid REITs that do not upgrade properties.
* Earnings: monitor earnings regularly; be prepared to sell when the market of property location weakens.
# Rebol Programming
## Foreword

This book covers the basics of Rebol programming, what Rebol actually does and why it's designed the way it is. It's not a reference manual and therefore doesn't contain a complete overview of all functions, but aims to teach the mechanics and principles of the language to give you a deeper understanding of it.

### Guide to readers

This is a wikibook, as such you should learn a bit about what it is and how it does its magic.
The book is (or will be) organized into different parts (chapters), but as this is a work that is always evolving, things may be missing or just not where they should be, you are free to become a writer and contribute to fix things up.

### Guide to writers

All Rebol developers who have interesting information are encouraged to come forward. It does not matter if you are not a stellar writer, as eventually it will be cleaned up. Although you can post to this book without registering, it is strongly advised that you do so so that we can discuss content which may be contentious.
It is advised at this point to try and keep meanings within the realm of common understanding by the REBOL community. Anything outside that realm should be stated as such.

#### Writing style

Function names in the text:
function
Code:

## Table of contents

* About Rebol
* Installing Rebol
* The console
* Internal utilities
* Programming in Rebol
* Rebol core manual (no graphic)
* VID guide (graphic for beginners)
* Rebol DRAW guide (drawing images and image manipulation)
* Rebol View guide (advanced graphic)
** Face object
** Face hierarchy
** Face functions
** Face events
** Face contents
** Face effects
** Special features
** Image datatype and manipulation
* Rebol and 3D
* Rebol as a web service: Quick and easy CGI
** Web forms
** Using cookies
** Making a BBS (Tutorial)
** Rebol and Apache
** Rebol and FastCGI
* Debugging techniques
* Design guide
* Rebol jargon
* Rebol and JSON
* Language features
* Advanced topics
* Third party tools
* Third party tutorials
* Developer resources
* Rebol internals
* Rebol examples
* All Rebol words (Dictionary)
# Piano/Rhythm

There are two essential pieces to music: rhythm and pitch. Pitch refers to how high or low a note is in tone, whereas rhythm refers to the arrangement of those tones. Since pitch can get fairly complicated, let us first discuss rhythm.

## Beats

A beat in the music is a "pulse." For instance, if you played one note on the piano, it might look like this:
# Piano/The Basics

The best way to learn to play the piano is, like most other things, practicing it daily or at least regularly. It is good to initially practice scales and chord cadences. To put your right hand in the position to play the C-G notes, put your fingers on the keyboard in the order shown in the image below:
You should memorize the notes in relation to black keys: B is not the seventh key from C, but it's the key on right side of the three black keys. Additionally, you should sit at the front of the bench (or chair, although it is recommended for you to get a piano bench or something that resembles it) and place the middle c key right in front of your bellybutton. The middle c key in the keyboards containing 61 keys is the white key after 3 sets of black keys (meaning that you'll count ten black keys starting from the left and put the white key right before the black one to the right in front of your navel) For regular pianos (88 keys), add an extra 6 black keys to the set of ten.
Sit down and play around for a bit; experiment, have fun. (Keep your wrists straight and relaxed.) It's best to have a real piano for this, but if one isn't available, at least make sure the keyboard you're using has touch sensitivity.
Your wrists should be straight and but your hand should be relaxed. Let your arm fall to your side, relaxed and parallel to the keys. Make your hand into a fist and then extend your fingers straight. Then relax and let your fingers fall. The result is the correct hand position. Of course this is only the starting position, in real playing it immediately flies out of the window. A relaxed hand has fingers that are slightly curved, a bit like how a hand looks resting over a computer mouse. This will allow you to play the black and white keys easily.
The first things you'll probably notice (if you don't know already) is that keys on the left are low, and keys on the right are high; also that playing two adjacent keys simultaneously sounds dissonant.
The number of keys may seem overwhelming at first, but their organization is simple -- they're in a repeating pattern of octaves, one of which is pictured above. Try finding one of the C notes in the middle of the keyboard. Now play another C above or below it -- you'll hear immediately why they have the same name.
The black keys are chromatic notes and used when the key requires notes that sound 'in-between' what you get when playing on the white keys.
# Piano/Rests

In this diagram are shown the seven different types of rests used in musical notation for pianos.
1. The rest with the 1 underneath is known as a big rest. This name is easily remembered with the fact that the rest drops under the line on the staff, making it a "hole". This rest takes up an four beats of music, the size of the standard measure.
2. The rest with the 1/2 underneath is known as a half rest. It consists of two beats, generally half a measure.
3. The rest with the 1/4 underneath it is a quarter rest. It consists of one beat, or one fourth of a standard measure.
4. The rest with the 1/8 underneath is known as an eighth rest. it consists of 1/2 of a beat, or 1/8 of a standard measure.
5. 1/16 – 16th rest; 1/4 of a beat, 1/16 of a measure
6. 1/32 – 32nd rest. rarely used. 1/8th of a beat, 1/32 of a measure
7. 1/64 – 64th rest. rarely used. 1/16 of a beat, 1/64 of a measure.
The 1/32 rest and 1/64 rest are rarely used in most pieces, with the exception of some slow pieces or pieces with irregular time signatures.
# Piano/Tied Notes

Tied notes are two notes in different measures that are played as one continuous note. A group of tied notes is written as two or more separate notes held together by a curved line call a tie. For example, if a composer wants to write a note that gets eight beats in 4/4 time, he would write to whole notes (four beats) in two measures and connect them with a tie. He could do the same with one more whole note to make a note with twelve beats, and so on and so forth.
# Piano/Time Signatures

Time signatures are the number of beats per measure
For example
2/4 = 2 beats per measure
3/4 = 3 beats per measure
4/4 = 4 beats per measure
Same applies for anything over 8 except there would be twice as many notes involved
# Piano/Treble Clef and Bass Clef

Music can be written in a variety of ways. Less intricate systems exist which only indicate the basic structure (chord changes) of a song and require the reader to already know the melody or improvise one, while more formal systems allow for carefully indicating each sound to make and also when to be tacit (silent), and the respective durations of each. The vast majority of Western music in the modern era is written using a system of notation where each sound is represented by a symbol called a note which is placed within an arrangement of five parallel lines running horizontally known as a staff, where the lines and spaces between them each correspond to a consecutive pitch (acoustic frequency) in a scale, with lower pitches at the bottom and higher ones at the top. The specific symbol used for each note indicates its duration, and other symbols called rests indicate the lengths of silence between them, if any.
The first symbol on every staff is a symbol called a clef, whose function is to identify one of the lines of the staff as representing a particular note. Pianos, able to play notes ranging over many octaves simultaneously, usually have music written with two staves, each with a different clef. The treble clef, or G clef, is used for the higher sounding notes, usually played with the right hand. The bass clef, or F clef, is used for the lower sounding notes, usually played with the left hand. When the two staves are joined on the left by a brace, they are collectively called a grand staff.
The right hand plays the treble clef the left hand plays the bass clef.
# Piano/Reading Music

Music originated a long time ago. The first notations were random dots on a page. We cannot tell the pitch of them. Slowly, it developed into one line, then the grand staff we see today.

## Reading Music

Music Notation is needed for the player to indentify what key to play at what time. Learning how to read music is an essential part of playing the piano. If you don't know how to read music, you may be stuck trying to learn a difficult song by ear, which can be made much easier by reading the sheet music. Music is read by lines. There are 5 lines on a clef, with 2 sets of these for the piano.
The upper clef is known as the treble clef or G clef, and the lower clef is the bass clef or F clef. There are a lot of notes to associate with their particular piano keys, and that can seem overwhelming when first learning to read sheet music.

### Mnemonics

Notes are considered in 3 parts: the notehead, the stem, and optionally the flag.
In the treble clef the first line from the bottom is E, the second line is G, then B, D, and F. Different mnemonics exist, one is Every Good Boy Does Fine, a second is Every Girl Buys Designer Fashions, a genderless version is Elephants Get Big Dirty Feet. You may also make your own. The spaces are F, A, C, E, which spells the word FACE.
In the bass clef the first line from the bottom is G, the second is B, D, F, and A. One mnemonic is Good Burritos Don't Fall Apart. The spaces are A, C, E, G. One mnemonic is All Cows Eat Grass.

## References

* ↑ "EGBDF - What does EGBDF stand for? The Free Dictionary". Retrieved August 19, 2019.
* ↑ "GBDFA - What does GBDFA stand for? The Free Dictionary". Retrieved August 19, 2019.
# Radiation Oncology/Bile duct

| Front Page: Radiation Oncology | RTOG Trials | Edit this |
| Bile Duct: Main Page | Resectable Disease | Adjuvant RT | Unresectable Disease | Clinical Trials | | |
Cholangiocarcinoma
* Staging
* Overview
** Pathology Literature
* Resectable Disease
** Surgical Literature
** Adjuvant RT Literature
* Unresectable Disease
** EBRT Literature
** Brachytherapy Literature
** Malignant Biliary Obstruction
* Randomized evidence