(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 544954, 9203] NotebookOptionsPosition[ 541924, 9084] NotebookOutlinePosition[ 542403, 9102] CellTagsIndexPosition[ 542360, 9099] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["HOW TO SOLVE IT", "Section", CellChangeTimes->{{3.632937092873903*^9, 3.6329371297523675`*^9}}], Cell[CellGroupData[{ Cell["\<\ Mitmesuguseid probleeme lahendades kohtame k\[UDoubleDot]llalt tihti \ \[UDoubleDot]lesandeid, mille puhul ei ole ette teada, kuidas antud \ \[UDoubleDot]lesannet lahendada. 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Mis on antud? Milles seisnevad \[UDoubleDot]lesande \ tingimused? \ \>", "Text", CellChangeTimes->{ 3.632940595536148*^9, {3.632940694986323*^9, 3.6329407171851616`*^9}}], Cell[CellGroupData[{ Cell["\<\ * Kas tingimusi saab rahuldada? Kas tingimused on otsitava m\[ADoubleDot]\ \[ADoubleDot]ramiseks piisavad? V\[OTilde]i on ebapiisavad? V\[OTilde]i \ vastuolulised? V\[OTilde]i on nende hulgas \[UDoubleDot]learuseid? \ \>", "Text", CellChangeTimes->{ 3.632940595536148*^9, {3.632940694986323*^9, 3.632940752612824*^9}}], Cell[CellGroupData[{ Cell["*Valmistage joonis. V\[OTilde]tke kasutusele sobiv \ t\[ADoubleDot]histus. ", "Text", CellChangeTimes->{ 3.632940595536148*^9, {3.632940694986323*^9, 3.632940774624462*^9}}], Cell["\<\ *Jagage tingimused osadeks. Kas saate neid osi \[UDoubleDot]les kirjutada? \ \>", "Text", CellChangeTimes->{ 3.632940595536148*^9, {3.632940694986323*^9, 3.632940777182867*^9}}] }, Open ]] }, Open ]] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["TEISEKS. leidke seos andmete ja otsitava vahel. ", "Text", CellFrame->{{0, 0}, {0, 3}}, CellChangeTimes->{{3.632941179711974*^9, 3.632941209866827*^9}, { 3.6329422907147255`*^9, 3.6329423009483433`*^9}}], Cell[CellGroupData[{ Cell["\<\ Kui vahetut seost ei \[OTilde]nnestu leida, siis olete sunnitud vaatlema abi\ \[UDoubleDot]lesandeid. \ \>", "Text", CellChangeTimes->{{3.632941179711974*^9, 3.632941193751999*^9}}], Cell[CellGroupData[{ Cell["K\[OTilde]ige selle tulemusena peate te koostama LAHENDUSPLAANI. ", \ "Text", CellChangeTimes->{{3.632941179711974*^9, 3.632941193751999*^9}, { 3.632942288858322*^9, 3.63294230470795*^9}}], Cell[CellGroupData[{ Cell["PLAANI KOOSTAMINE ", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.632941316695815*^9}}], Cell[CellGroupData[{ Cell["\<\ * Kas olete seda \[UDoubleDot]lesannet varem n\[ADoubleDot]inud? V\[OTilde]i \ olete n\[ADoubleDot]inud samasugust \[UDoubleDot]lesannet veidi teisel kujul? \ \>", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.6329413260246315`*^9}}], Cell[CellGroupData[{ Cell["\<\ * Kas teate m\[OTilde]nda antuga seostatavat \[UDoubleDot]lesannet? Kas teate \ m\[OTilde]nda teoreemi, mis v\[OTilde]iks siin vajalikuks osutuda?\ \>", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.632941335946248*^9}}], Cell[CellGroupData[{ Cell["\<\ * Vaadelge otsitavat! Ja p\[UDoubleDot]\[UDoubleDot]dke meenutada \ m\[OTilde]nda tuntud \[UDoubleDot]lesannet, milles on sama v\[OTilde]i \ sarnane otsitav. \ \>", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.6329413552434826`*^9}}], Cell[CellGroupData[{ Cell["\<\ * Siin ongi antuga seostatav ja varem lahendatud \[UDoubleDot]lesanne. Kas \ saate seda \[UDoubleDot]lesannet \[ADoubleDot]ra kasutada? Kas saate \ \[ADoubleDot]ra kasutada selle \[UDoubleDot]lesande tulemust? V\[OTilde]i \ tema lahendamise meetodit? Kas ei peaks sisse tooma m\[OTilde]ne abielemendi, \ mis v\[OTilde]imaldaks varem lahendatud \[UDoubleDot]lesannet \[ADoubleDot]ra \ kasutada? \ \>", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.6329413836667323`*^9}}], Cell[CellGroupData[{ Cell["\<\ * Kas \[UDoubleDot]lesannet saab teisiti s\[OTilde]nastada? Kas teda ei saaks \ veel teisiti s\[OTilde]nastada? P\[ODoubleDot]\[ODoubleDot]rduge tagasi \ definitsioonide poole. \ \>", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.632941394524351*^9}}], Cell[CellGroupData[{ Cell["\<\ * Kui te ei suuda antud \[UDoubleDot]lesannet lahendada, siis proovige k\ \[OTilde]igepealt lahendada m\[OTilde]ni temaga seostatav \ \[UDoubleDot]lesanne. Kas saate koostada antuga seostatava, kuid \ j\[OTilde]ukohasema \[UDoubleDot]lesande? V\[OTilde]i \[UDoubleDot]ldisema \ \[UDoubleDot]lesande? V\[OTilde]i erijuhu? V\[OTilde]i sarnase \ \[UDoubleDot]lesande? Kas suudate lahendada antud \[UDoubleDot]lesande mingi \ osa? S\[ADoubleDot]ilitage vaid osa tingimustest, j\[ADoubleDot]ttes \ \[UDoubleDot]lej\[ADoubleDot]\[ADoubleDot]nud k\[OTilde]rvale. \ Kuiv\[OTilde]rd on otsitav siis m\[ADoubleDot]\[ADoubleDot]ratud? Kuidas ta \ saab muutuda? Kas saate andmetest midagi kasulikku v\[ADoubleDot]lja lugeda? \ Kas saate esitada uued andmed, millest sobiva otsitava saaks m\[ADoubleDot]\ \[ADoubleDot]rata? Kas saate muuta otsitavat v\[OTilde]i andmeid v\[OTilde]i \ tarbekorral ka m\[OTilde]lemaid nii, et uus otsitav ja uued andmed oleksid \ teineteisele l\[ADoubleDot]hedasemad? \ \>", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.6329414083615756`*^9}}], Cell["\<\ * Kas kasutasite k\[OTilde]iki andmeid? Kas kasutasite k\[OTilde]iki \ tingimusi? Kas arvestasite k\[OTilde]iki \[UDoubleDot]lesandes sisalduvaid \ olulisi m\[OTilde]isteid? \ \>", "Text", CellChangeTimes->{{3.6329413085838003`*^9, 3.6329414083615756`*^9}}] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Closed]] }, Open ]] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["KOLMANDAKS - t\[ADoubleDot]itke oma lahendusplaan. ", "Text", CellFrame->{{0, 0}, {0, 3}}, CellChangeTimes->{{3.6329417068368998`*^9, 3.63294172413733*^9}}], Cell[CellGroupData[{ Cell["PLAANI T\[CapitalADoubleDot]ITMINE", "Text", CellChangeTimes->{{3.6329417068368998`*^9, 3.632941739409757*^9}}], Cell["\<\ * Lahendusplaani t\[ADoubleDot]itmisel kontrollige iga sammu. Kas selle sammu \ \[OTilde]igsus on teile selgelt n\[ADoubleDot]ha? Kas saate selle \ \[OTilde]igsust t\[OTilde]estada? \ \>", "Text", CellChangeTimes->{{3.6329417068368998`*^9, 3.6329417594557924`*^9}}] }, {2}]] }, Closed]], Cell[CellGroupData[{ Cell["NELJANDAKS - uurige saadud lahendit. ", "Text", CellFrame->{{0, 0}, {0, 3}}, CellChangeTimes->{{3.6329417068368998`*^9, 3.6329417812490306`*^9}}], Cell[CellGroupData[{ Cell["TAGASIVAADE", "Text", CellChangeTimes->{{3.6329417068368998`*^9, 3.6329417900786457`*^9}}], Cell[CellGroupData[{ Cell["\<\ * Kas saate kontrollida tulemust? Kas saate kontrollida \ lahendusk\[ADoubleDot]iku?\ \>", "Text", CellChangeTimes->{{3.6329417068368998`*^9, 3.6329418202334995`*^9}}], Cell[CellGroupData[{ Cell["\<\ * Kas saate tulemust teisiti leida? Kas ta pole \[ADoubleDot]kki vahetult n\ \[ADoubleDot]htav? \ \>", "Text", CellChangeTimes->{{3.6329417068368998`*^9, 3.6329418395463333`*^9}}], Cell["\<\ * Kas tulemust v\[OTilde]i lahendusk\[ADoubleDot]iku saab \[ADoubleDot]ra \ kasutada m\[OTilde]ne teise \[UDoubleDot]lesande korral? \ \>", "Text", CellChangeTimes->{{3.6329417068368998`*^9, 3.632941845021943*^9}}] }, Open ]] }, Open ]] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["\[CapitalUDoubleDot]lesandeid \ \[OpenCurlyDoubleQuote]Kuidas seda lahendada?\[CloseCurlyDoubleQuote] juurde", FontWeight->"Bold"]], "Subsection", CellChangeTimes->{{3.632940434746666*^9, 3.632940445994285*^9}, { 3.632940478177142*^9, 3.6329404956803727`*^9}, {3.6329989397299685`*^9, 3.6329989624904084`*^9}}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["1.", FontWeight->"Bold"], " Ajalehepaber on keskmiselt 0,05 mm paks. Kui me murrame ajalehe pooleks, \ saame kaks korda paksema ajalehe, s.o. 0,1 mm paksuse lehe. Kui saadud \ ajaleht veel kaheks kokku murda, siis saame 4 korda paksema ajalehe. Kui paks \ oleks ajaleht, mille me saaksime peale 25-ndat lehe kokku murdmist? \ K\[OTilde]igepealt pakkuge v\[ADoubleDot]lja tulemuse prognoos, seej\ \[ADoubleDot]rel arvutage v\[ADoubleDot]lja selle lehepaki paksus." }], "Text", CellChangeTimes->{{3.632940526490427*^9, 3.6329405421216545`*^9}, { 3.632941096173827*^9, 3.6329411277638826`*^9}, {3.6329989992908735`*^9, 3.632999164354763*^9}, {3.6329999266265025`*^9, 3.632999949028142*^9}, { 3.63299999902623*^9, 3.633000008027446*^9}, {3.633000045966712*^9, 3.633000105356016*^9}, {3.6330015785758038`*^9, 3.633001636139905*^9}, 3.633001763451729*^9}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["2.", FontWeight->"Bold"], " L\[ADoubleDot]htudes punktist P liikus karu \[UDoubleDot]he miili otse l\ \[OTilde]unasse. Seej\[ADoubleDot]rel muutis ta suunda ja liikus \ \[UDoubleDot]he miili itta. Seej\[ADoubleDot]rel \ p\[ODoubleDot]\[ODoubleDot]rdus ta j\[ADoubleDot]lle vasakule, liikus \ \[UDoubleDot]he miili otse p\[OTilde]hja suunas ja j\[OTilde]udis tagasi l\ \[ADoubleDot]htepunkti P. Mis v\[ADoubleDot]rvi oli see karu?" }], "Text", CellChangeTimes->{{3.632940526490427*^9, 3.6329405421216545`*^9}, { 3.632941096173827*^9, 3.6329411277638826`*^9}, {3.6329989992908735`*^9, 3.632999164354763*^9}, 3.6330001103792253`*^9}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["3. ", FontWeight->"Bold"], "Kolme kanamuna keetmiseks kulub 6 minutit. Mitu minutit kulub kaheksa \ kanamuna keetmiseks? \[LineSeparator]Veidi keerukam \[UDoubleDot]lesanne: \ \[OpenCurlyDoubleQuote]Kui poolteist kana muneb pooleteist \ p\[ADoubleDot]evaga poolteist muna, siis kui mitu muna muneb 9 kana 9 p\ \[ADoubleDot]evaga?\[CloseCurlyDoubleQuote]" }], "Text", CellChangeTimes->{ 3.6330001417196803`*^9, {3.633000176788542*^9, 3.633000221981821*^9}, { 3.6330085582879887`*^9, 3.6330085584479885`*^9}, {3.633008682868163*^9, 3.6330087606282716`*^9}}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["4.", FontWeight->"Bold"], " Robert tahab osta t\[UDoubleDot]ki t\[ADoubleDot]iesti tasast maad, millel \ oleks neli rajajoont. Kaks rajajoont peavad suunduma p\[OTilde]hjast l\ \[OTilde]unasse, \[UDoubleDot]lej\[ADoubleDot]\[ADoubleDot]nud kaks aga idast \ l\[ADoubleDot]\[ADoubleDot]nde ja iga rajajoone pikkus peab olema 100 \ meetrit. Kas Robert saab Eesti piirides sellise maat\[UDoubleDot]ki osta?" }], "Text", CellChangeTimes->{{3.632940526490427*^9, 3.6329405421216545`*^9}, { 3.632941096173827*^9, 3.6329411277638826`*^9}, {3.6329989992908735`*^9, 3.632999164354763*^9}, {3.632999213136049*^9, 3.6329994015063796`*^9}, { 3.632999758871807*^9, 3.632999810414298*^9}, 3.633000257003883*^9}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["5. ", FontWeight->"Bold"], "Vanaisa paberite hulgast leiti selline arve:\n\t72 kalkunit _67.9_ $.\n\ Ilmselt on nende kodulindude koguhinda kujutava arvu esimene ja viimane \ number loetamatuks kustunud ning on n\[UDoubleDot]\[UDoubleDot]d siin \ asendatud kriipsukestega. Millised olid need kaks kustunud numbrit ja kui \ palju maksis \[UDoubleDot]ks kalkun?" }], "Text", CellChangeTimes->{{3.632940526490427*^9, 3.6329405421216545`*^9}, { 3.632941096173827*^9, 3.6329411277638826`*^9}, {3.6329989992908735`*^9, 3.632999164354763*^9}, {3.632999213136049*^9, 3.6329994015063796`*^9}, { 3.632999439851247*^9, 3.632999728904155*^9}, 3.6330002597806873`*^9}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["6.", FontWeight->"Bold"], " Peale aastatepikkust \[ADoubleDot]raolekut tuli Sherlock Holmes tagasi \ Inglismaale ja l\[ADoubleDot]ks k\[UDoubleDot]lla oma vanale s\[OTilde]brale \ doktor Watsonile. Nad istusid avatud akna all. \[CapitalOTilde]uest kostis \ laste k\[ADoubleDot]ratsemist. \nHolmes: \[OpenCurlyDoubleQuote]\ \[CapitalODoubleDot]elge palun, kui palju teil lapsi on?\ \[CloseCurlyDoubleQuote] \nWatson: \[OpenCurlyDoubleQuote]Seal ei ole ainult \ minu lapsed, vaid on ka minu venna, \[OTilde]e ja onu lapsed. Nad teevad l\ \[ADoubleDot]rmi sellep\[ADoubleDot]rast, et neid ei ole nii palju, et saaks \ kokku panna kahte \[UDoubleDot]heksaliikmelist laptuumeeskonda. Minul on k\ \[OTilde]ige rohkem lapsi, vennal on v\[ADoubleDot]hem, \[OTilde]el veel v\ \[ADoubleDot]hem ja onul on k\[OTilde]ige v\[ADoubleDot]hem lapsi. Kui laste \ arvud korrutada, siis te saate minu maja numbri, mida te siia tulles ilmselt \ n\[ADoubleDot]gite. Ehk \[UDoubleDot]tlete n\[UDoubleDot]\[UDoubleDot]d ise, \ kui mitu last on minul, minu vennal, \[OTilde]el ja onul?\ \[CloseCurlyDoubleQuote] \nPeale l\[UDoubleDot]hikest m\[OTilde]ttepausi s\ \[OTilde]nas Holmes: \[CloseCurlyDoubleQuote]Teie k\[UDoubleDot]simusele \ vastamiseks pean esitama \[UDoubleDot]he t\[ADoubleDot]iendava \ k\[UDoubleDot]simuse: \[OpenCurlyDoubleQuote]Kas teie onul on \[UDoubleDot]ks \ laps?\[CloseCurlyDoubleQuote]\[CloseCurlyDoubleQuote] \nMe ei tea, mida \ Watson Holmesile vastas. Teame ainult, et peale vastuse saamist lahendas \ Holmes \[UDoubleDot]lesande. Ja n\[UDoubleDot]\[UDoubleDot]d \ k\[UDoubleDot]simused: \n\[OpenCurlyDoubleQuote]Kui palju lapsi oli igas \ perekonnas lapsi? Mis numbriga majas elas Watson?\[CloseCurlyDoubleQuote]" }], "Text", CellChangeTimes->{{3.632940526490427*^9, 3.6329405421216545`*^9}, { 3.632941096173827*^9, 3.6329411277638826`*^9}, {3.6329989992908735`*^9, 3.632999164354763*^9}, {3.632999213136049*^9, 3.6329994015063796`*^9}, { 3.632999758871807*^9, 3.632999810414298*^9}, 3.633000257003883*^9, { 3.6330003514620485`*^9, 3.633000399229333*^9}, 3.633008640988104*^9}], Cell[TextData[{ StyleBox["7.", FontWeight->"Bold"], " Eesel Iiahil on oaasis 45 arbuusi. Ta peab viima v\[OTilde]imalikult palju \ arbuuse 15 miili kaugusel olevasse linna. Korraga suudab Iiah kanda 15 \ arbuusi. Et eesel ei ole n\[OTilde]us liikuma ilma toiduta, siis ta s\ \[ODoubleDot]\[ODoubleDot]b iga miili kohta \[UDoubleDot]he arbuusi. Kui mitu \ arbuusi suudab Iiah linna viia?\[CloseCurlyDoubleQuote] " }], "Text", CellChangeTimes->{ 3.6330004771826696`*^9, {3.6330005329059677`*^9, 3.6330005637160215`*^9}}] }, Closed]] }, Closed]] }, Closed]] }, Closed]] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["L\[OTilde]petuseks", FontWeight->"Bold"]], "Subsection", CellChangeTimes->{{3.632940434746666*^9, 3.632940445994285*^9}, { 3.632940478177142*^9, 3.6329404956803727`*^9}, {3.6329989397299685`*^9, 3.6329989624904084`*^9}, {3.6330096994938316`*^9, 3.633009702582637*^9}}], Cell[BoxData[{ GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJzsvXV4Fcf7/o8VWqAUKBDc3a24BRI0uLs7BC3u7u5W3CW4FinuENxdgmtp 3y1nf6/vPr8z17LnJEiTAv3M/cdee/bMjs9zP/fs7GySBm0qNAkTKlSoDt9y qFC/s2f79vW7VgzHj8JdOzZuEJaTq6FDhepOmP93bmhoaGhoaGhoaGhoaGho aGhoaGhoaGhoaGhoaGhoaGhoaGhoaGhoBIK3b99yfP78+blz527fvt2xY8f5 8+dz5a+//nI4HJ87dxoa/1mo8eX4MLw1wcmTJ08uXbp0/fr1a9eu3bhxg/Oz 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