A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal. A problem implies a desired outcome coupled with an apparent deficiency, doubt or inconsistency that prevents the outcome from taking place.

Problem solving[link]

Every theoretical problem asks for an answer or solution. Trying to find a solution to a problem is known as problem solving. There are many standard techniques for problem solving, such as Proof by Contradiction, or Proof by Exhaustion, the latter famously being used in the solution to the Thirty-Six Officers Problem posed by Leonhard Euler. A problem is a gap between an actual and desired situation. The time it takes to solve a problem is a way of measuring complexity.^[1] Many problems have no discovered solution and are therefore classified as an open problem.

From the mid 20th century, the field of theoretical computer science has explored the use of computers to solve problems.

Examples[link]

• Mathematical problem is a question about mathematical objects and structures that may require a distinct answer or explanation or proof. Examples include word problems at school level or deeper problems such as shading a map with only four colours.
• In society, a problem can refer to particular social issues, which if solved would yield social benefits, such as increased harmony or productivity, and conversely diminished hostility and disruption.
  See also: Wicked problem
• In business and engineering, a problem is a difference between actual conditions and those that are required or desired. Often, the causes of a problem are not known, in which case root cause analysis is employed to find the causes and identify corrective actions.
• In chess, a problem is a puzzle set by somebody using chess pieces on a chess board, for others to get instruction or intellectual satisfaction from determining the solution.
• In theology, there is what is referred to as the Synoptic Problem, regarding the Gospels' relationship to each other.
• In academic discourse a problem is a challenge to an assumption, an apparent conflict that requires synthesis and reconciliation. It is a normal part of systematic thinking, the address of which adds to or detracts from the veracity of a conclusion or idea.
• An optimization problem is finding the best solution from all feasible solutions. A good example of this type of problem is the travelling salesperson problem which is based on calculating the most efficient route between many places
• In computability theory a decision problem requires a simple yes-or-no answer.
• In rock climbing a problem is a series of rocks that forces the climber to climb.
• In reading, a problem is a combination of a series of words with the overall plotline, which the reader must attempt to decipher.
• In walking, a mobility problem is presented. Motion is achieved via mechanical interaction of the legs and a surface.

See also[link]

• Heuristic
• How to Solve It
• Question
• Problem-based learning
• Problematization
• Worry

External links[link]

• Problems Problem brainstorming site with tools to solve them.

References[link]

Natalia Kills
Natalia Kills in 2011.
Background information
Birth name	Natalia Keery-Fisher
Also known as	Verbz, Verbalicious,[1] Natalia Noemi Cappuccini,[2] Verse, Candy Rapper, Verbal
Born	(1986-08-15) 15 August 1986 (age 25) Bradford, West Yorkshire, England
Genres	Pop, electropop
Occupations	Singer-songwriter, actress, film director
Instruments	Vocals, drums, guitar
Years active	1995–present
Labels	Adventures in Music, will.i.am, Cherrytree, Interscope
Website	www.nataliakills.com

Natalia Keery-Fisher^[3][4] (born 15 August 1986) is an English singer-songwriter, actress, and director who performs under the stage name Natalia Kills. She released her debut album, Perfectionist, in 2011.

Biography[link]

1986–94: Early life[link]

Kills was born in Bradford, West Yorkshire, to an Afro-Jamaican father and Uruguayan mother,^[5] where she attended Bradford Girls' Grammar School. In addition, she studied classical drama at the London Academy of Music and Dramatic Art.^[3] She stated in a post on her blog on social website, MySpace that she grew up flying between London and Florida, where she had relatives, resulting in a mixed American and English accent.^[6]

1995–2010: Career beginnings[link]

Kills made her acting debut at age 9 in 1995 in New Voices. She had a regular role as Sima on the TV sitcom All About Me and also played Amy Franks in the BBC's long-running radio drama The Archers. She began writing songs at 14,^[7] some of which were featured in films and television shows, including Bring It On 4, Sleepover, Just My Luck, and Entourage.^[4] After finishing with The Archers in 2003, Kills began pursuing a music career and attributes her musical breakthrough to winning a Radio 1 MC Battle in Leeds under the name "Candy Rapper" in 2003.^[3] She signed to the UK record company Adventures in Music and released her first single "Don't Play Nice" under the name Verbalicious in February 2005. Kills' told W that her childhood nickname from her mother was "Verbal" because she talked and sang a lot. She adopted the name and variations of it as her stage name at some points during her career.^[8]

While writing music for films,^[9] Kills posted her self-produced and written demo extended play, Wommanequin on music social website MySpace in 2007 that attracted the attention of blogger Perez Hilton in 2008, her song received 2 million plays on the website and Kills reached the top of the unsigned artists chart.^[8] With offers coming in for concerts and festivals, Kills moved to Los Angeles.^[9] In LA, Kills was approached by producers, A&R and labels with contracts.^[9][10] A DJ introduced her to will.i.am after hearing her demo and learning that she did not have a record deal. In January 2008, will.i.am signed her to his record label, will.i.am Music Group. She did not sign right away as she had reservations about the music industry and will.i.am had to go to London a month later to convince her to record with him.^[9] During this time she also co-wrote and appeared on "They Talk Shit About Me" by French recording artist M. Pokora and met underground director Guillaume Doubet, who would go on to direct many of her videos, in Paris.

[edit] 2011—: Perfectionist

Kills explained in an interview that she adopted the stage name Natalia Kills at the behest of her record company, which found "Natalia Cappuccinni" hard to pronounce.^[9] She had taken on her grandmother's family name a few years prior.^[6] She explained in an interview that her stage name is based on the phrase "you killed it," and represents her tendecy to be a perfectionist.^[11] Kills released her debut album Perfectionist in April 2011 in Germany following a top ten placing by the first single, "Mirrors". The album was described as a concept album by Kills, chronicling the fact that perfection is attainable.^[7] It features production by Jeff Bhasker and Fernando Garibay,^[7] who had worked with Lady Gaga.^[12] The album was accompanied by four singles, "Mirrors", "Wonderland", "Free" and "Kill My Boyfriend". The first three singles were minor hits in some European countries but failed to chart in the US or UK. Kills opened for Kelis' European All Hearts Tour, as well as supported Robyn on her Body Talk Tour in November 2010 and early 2011. She also supported Ke$ha on the UK leg of her Get Sleazy Tour. Throughout August and September 2011, Kills supported Katy Perry on her California Dreams Tour for eight dates in Europe^[13] and São Paulo, Brazil. She also opened for the Black Eyed Peas over the summer of 2011 in Europe.^[8][11]

Kills is featured on a Junior Caldera's single, "Lights Out (Go Crazy)", along with Far East Movement. It was released on March 13, 2012.^[14] Kills also features in Tatana's single, "You Can't Get In My Head (If You Can't Get In My Bed)".

On April 4, 2012, the singer took to Twitter to announce she was back in the studio, potentially beginning work on her second studio album.

Influences[link]

Kills called Kate Bush and Alanis Morissette her most important musical influences, highlighting them as emotional artists who wrote honestly about their own experiences.^[15] She has also gone on to cite Gwen Stefani as her hero. She also claims that Depeche Mode, Prince, Vanity 6 and Freddie Mercury inspire her live performances.^[11]

Discography[link]

• Perfectionist (2011)

Filmography[link]

References[link]

External links[link]

• Official website
• Natalia Kills at Allmusic
• Natalia Kills at the Internet Movie Database

Wiz Khalifa
Wiz Khalifa in Brooklyn, New York in August 2009.
Background information
Birth name	Cameron Jibril Thomaz
Born	(1987-09-08) September 8, 1987 (age 24) Minot, North Dakota, United States
Genres	Hip hop
Occupations	Rapper, singer, songwriter, actor
Years active	2005–present
Labels	Rostrum, Taylor Gang, Warner Bros., Atlantic
Associated acts	Snoop Dogg, Rick Ross, Curren$y, Big Sean, Chevy Woods, Mac Miller, Juicy J, Tinie Tempah, Yelawolf, Maroon 5, Big K.R.I.T.
Website	wizkhalifa.com

Cameron Jibril Thomaz (born September 8, 1987), better known by the stage name Wiz Khalifa, is an American rapper. He released his debut album, Show and Prove, in 2006, and signed to Warner Bros. Records in 2007. His Eurodance-influenced single, "Say Yeah", received urban radio airplay, charting on the Rhythmic Top 40 and Hot Rap Tracks charts in 2008.^[1] Khalifa parted with Warner Bros. and released his second album, Deal or No Deal, in November 2009. He released the mixtape Kush and Orange Juice as a free download in April 2010; he then signed with Atlantic Records.^[2] He is also well known for his debut single for Atlantic, "Black and Yellow", which peaked at number 1 on the Billboard Hot 100. His debut album for the label, Rolling Papers, was released on March 29, 2011.^[3]

Early life[link]

Khalifa was born on September 8, 1987 to a mother and a father serving in the military.^[1][4] His parents divorced when Khalifa was about three years old. His parents' military service caused him to move regularly: Khalifa lived in Germany, the United Kingdom, and Japan before settling in Pittsburgh where he attended Taylor Allderdice High School.^[1][4]

His stage name is derived from khalifa, an Arabic word meaning "successor", and wisdom, which was shortened to Wiz when Khalifa was a young boy .^[5] Khalifa stated to spinner.com that the name also came from being called "young Wiz 'cause I was good at everything I did, and my granddad is Muslim, so he gave me that name; he felt like that's what I was doing with my music." He got his stage name tattooed on his 17th birthday.^[6][7] He includes Jimi Hendrix, Camp Lo, The Notorious B.I.G. and Bone Thugs-n-Harmony among his influences.^[8]

Career[link]

[edit] 2005–08: Early mixtapes and Show and Prove

Rostrum Records president Benjy Grinberg first heard about Wiz Khalifa in 2004 when the rapper's contribution to a mixtape of various new Pittsburgh artists attracted his interest.^[9] When Grinberg finally met the 16-year-old artist, he immediately decided he wanted to work with him, later telling HitQuarters: "Even though he wasn’t all the way developed you could just tell that he was a diamond in the rough, and that with some polishing, guidance and backing he could become something special."^[9] Khalifa signed to the label shortly after and began a seven year period of artist development.^[9]

Khalifa released his first mixtape, Prince of the City: Welcome to Pistolvania, in 2005. The mixtape paved the way for his first full length album entitled Show and Prove in 2006. Khalifa was declared an "artist to watch" that year in Rolling Stone magazine.^[10][11]

In 2007, Khalifa signed to Warner Bros. Records and released two mixtapes through Rostrum Records: Grow Season, hosted by DJ Green Lantern and released on July 4, 2007, and Prince of the City 2, released on November 20, 2007. His debut Warner Bros. single "Say Yeah" reached number 25 on the Billboard Rhythmic Top 40 music chart and number 20 on Billboard's Hot Rap Tracks. The song samples "Better Off Alone" by Alice Deejay. Khalifa's vocals from "Say Yeah" appear near the end of Pittsburgh mash up producer Girl Talk's 2008 album, Feed the Animals, over music from Underworld's "Born Slippy", Usher's "Love in This Club", and the Cure's "In Between Days".^[12] Khalifa appeared with The Game, David Banner and Play-n-Skillz at U92's Summer Jam at the USANA Amphitheatre in West Valley City, Utah on August 2, 2008.^[13] Khalifa released the mixtapes Star Power in September 2008, and Flight School in April 2009 on Rostrum Records.

Khalifa parted ways with Warner Bros. Records in July 2009 after numerous delays in releasing his planned debut album for the label, First Flight. Khalifa stated to the Pittsburgh Post-Gazette that, "I learned a lot during my time there and matured as an artist during the process. I'm happy to be moving on with all of my material and having the chance to be in control of my next moves".^[14] Khalifa appeared with Girl Talk, Modey Lemon, Donora, Grand Buffet, and Don Caballero at the Amphitheatre at Station Square in Pittsburgh on July 31, 2009, where he announced that his relationship with Warner Bros. was over.^[15]

Wiz Khalifa performing at Columbia University in New York City in April 2010.

[edit] 2009–10: Deal or No Deal

Continuing his association with Rostrum Records, Khalifa released the single "Teach U to Fly", and the mixtape How Fly, a collaboration with New Orleans rapper Curren$y, on August 9, 2009.^[14] Khalifa introduced a more melodic style on the mixtape, alternating between singing and rapping. He opened for Wu-Tang Clan member U-God at the 2009 CMJ Music Marathon in New York City.^[16] Khalifa released the mixtape Burn After Rolling on November 2, 2009, where he raps over familiar beats from other artists, including the songs "If I Were A Boy" and "Diva" by Beyoncé, "Walking on a Dream" by Empire of the Sun, "Luchini AKA This Is It" by Camp Lo, and "Best I Ever Had" by Drake.^[17] Khalifa released his second album, Deal or No Deal, on November 24, 2009.^[18]

Khalifa performed at Emo's in Austin, Texas in March 2010 as part of the 2010 South by Southwest Music Festival.^[19] He appeared on the cover of XXL magazine that same month, for the magazine's annual list of Top 10 Freshman, which included Donnis, J. Cole, Pill, Freddie Gibbs, and Fashawn. Wiz Khalifa was named 2010 "Rookie Of The Year" by "The Source", with alongside Rick Ross, "The Man Of The Year".^[20] He toured with rapper Yelawolf on a 20-date tour, the Deal Or No Deal Tour.^[21] Khalifa released the free mixtape Kush and Orange Juice for download on April 14, 2010. Due to Khalifa's devoted grassroots fan base, the mixtape became the No. 1 trending topic on Twitter with the hash tag #kushandorangejuice, and "Kush and Orange Juice download” ranked No. 1 on Google’s hot search trends.^[22]

2010: Signing with Atlantic Records[link]

Citing music industry insiders, New York magazine wrote that Khalifa signed with Atlantic Records in April 2010, although the rapper did not confirm it.^[23] He stated to AllHipHop in June 2010 that he was working on a new album, but was weighing his options and had not yet decided on a label to distribute it.^[24] Khalifa confirmed to MTV on July 30 that he was signing an Atlantic Records deal.^[25]

Wiz Khalifa on stage in Boston in August 2010.

Khalifa was featured in a remix and video for the 2010 Rick Ross single "Super High", alongside Curren$y.^[26] He guested on the mixtape Grey Goose, Head Phones, and Thirsty Women by St. Louis rapper M.C,^[27] and was featured on the track "The Breeze (Cool)" on rapper Wale's August 2010 mixtape More About Nothing.^[28] Khalifa was named MTV's Hottest Breakthrough MC of 2010, winning with nearly 70,000 votes, and beating out finalists Nicki Minaj, J. Cole, Travis Porter, and Diggy Simmons.^[29]

Khalifa appeared at the Soundset 2010 festival in May 2010 in Minneapolis, Minnesota, alongside Method Man & Redman, Del the Funky Homosapien and Hieroglyphics, Atmosphere, Murs, Cage, and others.^[30] He also performed at the 2010 Rock the Bells festival, along with hip hop veterans Wu-Tang Clan, Snoop Dogg, Lauryn Hill, A Tribe Called Quest, Rakim, KRS-One, Jedi Mind Tricks and Slick Rick.^[31] Khalifa declined an invitation to tour with rapper Drake and launched his own "Waken Baken" tour, a 50-city national tour with rapper Yelawolf. The tour, scheduled to last from September to November 2010, has, as of October, sold out every venue.^[8] On November 2010, during his "Waken Baken" tour at East Carolina University, Wiz Khalifa was arrested for possession and trafficking of marijuana. He was then released the next morning after a $300K bail, and resumed his tour. Khalifa performed in a cypher during the 2010 BET Hip-Hop Awards. He recited his verse from the song, "The Check Point", from his mixtape with Curren$y, How Fly.^[32]

[edit] 2010–11: Mainstream success and Rolling Papers

Wiz Khalifa at SXSW in 2010

Khalifa released "Black and Yellow", his first single for Rostrum/Atlantic, produced by Stargate, which has received radio airplay.^[8][33] The single was peaked at number 1 on the Billboard Hot 100; the title of the song refers to the colours of the City of Pittsburgh.^[34] Khalifa released his debut album with Atlantic Records in 2011.^[35] He appeared with Curren$y on the track "Scaling the Building" on producer Ski Beatz' 2010 album, 24 Hour Karate School.^[36] Khalifa's record label is Taylor Gang Records, named after his love of Chuck Taylor All-Stars^[8], and Taylor Allderdice High School in Pittsburgh, PA, where he graduated from.

On March 29, 2011, Khalifa released his first studio album, Rolling Papers. The album debuted at number two on the US Billboard 200 chart, with first-week sales of 197,000 copies in the United States.^[37] Shortly afterward on March 31, 2011 Wiz Khalifa performed at Emory University in Atlanta, Georgia as part of the school's annual Dooley's Weekend.^[38] On June 26, 2011, Khalifa was nominated and won Best New Artist at the BET Awards of 2011.^[39] Khalifa collaborated with British rapper Tinie Tempah whom Tinie announced in an interview with Rolling Stone that his next single is to be called "Till I'm Gone" and would feature Wiz Khalifa and is to be produced by Stargate.^[40][41] The single and the video song were released at the end of June 2011.^[42]

Personal life[link]

Thomaz proposed to model Amber Rose on March 1, 2012 showing off the ring on Twitter.^[43] He is personal friends with Snoop Dogg, Juicy J, Yelawolf, and fellow Pittsburgh rapper Mac Miller.^[44]

In March 2012, Thomaz purchased a 2.8 private wooded acres with a 3,891-square-foot residence in Canonsburg, Pennsylvania, a small community southwest of Pittsburgh. The residence includes 5-bedroom, 4-bath eco-friendly, Brazilian Koa floors, stainless steel appliances, a separate guest house, and a lavish master suite with high ceilings.^[45] He currently resides there with his fiancée Amber Rose.

Discography[link]

Studio albums

• 2006: Show and Prove
• 2009: Deal or No Deal
• 2011: Rolling Papers
• 2012: O.N.I.F.C. ^[11][46][47]

Collaborative albums

• 2011: Mac & Devin Go to High School (with Snoop Dogg)
• 2012: TBA (with Taylor Gang)

Awards and nominations[link]

References[link]

External links[link]

Wikimedia Commons has media related to: Wiz Khalifa

• Official website
• Wiz Khalifa on Facebook
• Wiz Khalifa on Myspace
• Wiz Khalifa on Twitter
• Wiz Khalifa at MTV
• Non-commercial Wiz Khalifa mixtapes

Kendrick Lamar Duckworth^[1] (born June 17, 1987), simply known as Kendrick Lamar, is an American rapper and songwriter from Compton, California currently signed to Top Dawg, Aftermath and Interscope. He first gained major attention after the release of his 2010 mixtape Overly Dedicated. In 2011, his album Section.80, released exclusively through iTunes, instantly ranked as one of the top digital hip hop releases of the year.^[2] Lamar has amassed a large internet following, is a member of hip hop collective Black Hippy, along with Jay Rock, Schoolboy Q and Ab-Soul, and has worked with Snoop Dogg, Dr. Dre, Wiz Khalifa, Game, Drake, Busta Rhymes and Tech N9ne among other popular artists.^[3]

Biography[link]

1987-2009: Early life and career beginnings[link]

Kendrick Lamar was born in Compton, California, a community southeast of Los Angeles city limits, to parents from Chicago, Illinois.^[4] At the age of eight, in 1995, Lamar witnessed his idols, Tupac Shakur and Dr. Dre film the music video for their hit single "California Love," a very significant moment in Lamar's life.^[5] In 2003 at the young age of sixteen, Lamar released his first mixtape, Youngest Head Nigga In Charge under the name K. Dot.^[6] The mixtape was able to garner enough attention for Lamar to get a record deal with Top Dawg Entertainment, a Los Angeles-based independent record label.^[6] He then released a twenty-six track mixtape two years later titled Training Day.^[7] More recognition came Lamar's way after a video of a Charles Hamilton show surfaced, where Hamilton goes in the crowd and battles rappers at attendance. Lamar didn't hesitate and began rapping a verse over Milkbone's "Keep It Real", that would later appear on a track titled "West Coast Wu-Tang".^[5] In 2008 Lamar made a cameo appearance on Jay Rock's "All My Life (In the Ghetto)" music video. After receiving a co-sign from Lil Wayne, he released his third mixtape in 2009 titled C4, heavily themed around Tha Carter III LP.^[8] Soon after, he decided to drop his stage name K. Dot and go by his real name. This resulted in him releasing a self-titled EP; the Kendrick Lamar EP in late 2009.^[9]

[edit] 2010–2011: Overly Dedicated and Section.80

Kendrick performing at a concert in Toronto, Canada

In 2010 he toured with Tech N9ne and Jay Rock on The Independent Grind tour.^[6] On September 23, 2010 he released O(verly) D(edicated) a highly acclaimed mixtape that included a song titled "Ignorance is Bliss" in which he glorifies gangsta rap and street crime but ends each verse with "ignorance is bliss" giving the message "we know not what we do".^[10][11] It was that song specifically that made hip hop producer Dr. Dre want to work with Lamar.^[12] This led to him working with Dre and Snoop Dogg on Dre's Detox album and him considering signing to Aftermath Entertainment.^[6][13] In January 2011 Lamar said his debut album was 90% finished.^[6]

In early 2011 Lamar was featured on XXL Magazine's 2011 Freshman cover along with CyHi the Prynce, Meek Mill, Mac Miller, Yelawolf, Lil B, Big K.R.I.T. and Diggy Simmons among others.^[14] On July 2, 2011, Lamar released his third solo project Section.80 to critical acclaim. It features guest appearances from GLC, Colin Munroe, Schoolboy Q, Ab-Soul and includes production from longtime collaborator Sounwave, Wyldfyer, Terrace Martin, J. Cole and more. On the topic of whether Section.80 would be an album or a mixtape Lamar said "I treat every project like it’s an album anyway. It’s not gonna be nothing leftover. I never do nothing like that. These are my leftover songs y’all can have ‘em, nah. I’m gonna put my best out. My best effort. I’m tryna look for an album in 2012". The first single for Section.80 was the J. Cole produced track "HiiiPower", of which the concept was to further explain the HiiiPower movement. Section.80 went on to sell over 10,000 copies in its first week^[15] without any television or radio coverage and received many very positive reviews. In the second half of 2011, Lamar appeared on Game's The R.E.D. Album, Tech N9ne's All 6's and 7's, 9th Wonder's The Wonder Years and Drake's Take Care.

In August 2011, while onstage with Snoop Dogg, Dr. Dre and Game, at the West Los Angeles concert, the three of them crowned him the "New King of the West Coast"^[16]

[edit] 2012–present: Good Kid in a Mad City

On February 15, 2012, a song titled "Cartoons & Cereal" featuring Gunplay of Triple C's was leaked.^[17] Lamar revealed later that the track was for his upcoming album and he was planning to shoot a video for it.^[18]

In March 2012, MTV announced that Top Dawg Entertainment, the independent record label Lamar is signed to, have closed a joint venture deal with Interscope Records and Aftermath Entertainment, marking the end of his career as an independent artist. Under the new deal, Kendrick Lamar’s projects, including his upcoming debut studio album Good Kid in a Mad City will be jointly released via Top Dawg, Aftermath and Interscope, while releases from the rest of Black Hippy will be distributed via Top Dawg and Interscope.^[19]

Lamar premiered "The Recipe", his debut single and the lead single from Good Kid in a Mad City, at Power 106 on April 2, 2012. The track was released for digital download the following day. The song was produced by Scoop DeVille and features Dr. Dre.^{[citation needed]}

It was announced on May 14, 2012, that Lamar is working on a collaborative album with J. Cole. In an interview with Bootleg Kev, Cole stated that "I just started working with Kendrick the other day. We got it in, finally, again. We got maybe four or five [songs] together."

Personal life[link]

In high school, Centennial in Compton, Lamar was a good student.^[4] Lamar said that he has seen relatives who have died in his dreams for years. Tupac Shakur is also his favorite rapper, and influences not only his music, but his day-to-day lifestyle as well. In terms of subject matter, Kendrick Lamar has often been compared to Tupac Shakur. ^[6][20][21] He revealed that his favorite and most influential rappers are Tupac Shakur, The Notorious B.I.G., Nas, Jay-Z and his label-mate Eminem.

Discography[link]

• Section.80 (2011)
• Good Kid in a Mad City (2012)

References[link]

External links[link]

• Kendrick Lamar on Twitter
• kedricklamar.com Official Site