Indlela yokusombulula isikwere magic (Grade 3)? Iinzuzo kubafundi

iiphazili Mathematical zikhona inani emangalisayo. Ngamnye kubo ekhethekileyo indlela yabo, kodwa umtsalane yabo ixhomekeke kukuba ekugqibeleni isicombululo kuza kufuneka ukuza iifomyula. Kakade ke, sinako ukuzama uzisombulule, njengoko bathi, ngequbuliso, kodwa kuya kubakho ixesha elide kakhulu yaye phantse akukho nempumelelo.

Eli nqaku liza kuthetha enye yezi iimfihlakalo, kodwa ukuba ngqo - yesikwere magic. Sihlalutya ngokweenkcukacha indlela yokucombulula isikwere ngomlingo. 3 iklasi kwenkqubo ebanzi, Kakade ke, ukuba uhamba, kodwa mhlawumbi hayi wonke umntu wayeqonda okanye akazange ukukhumbula.

Yintoni na le mfihlelo?

Magic square, okanye njengoko ibizwa ngokuba, imilingo - itafile apho inani lwemihlathi kunye noluhlu ngokufanayo, yaye bonke bazaliswa amanani ezahlukeneyo. Umngeni engundoqo amanani kwisixa nkqo, tye kunye nemigca elinganayo siya kuwahlawulela efanayo.

Ukongeza isikwere magic, kukho naye semi-imilingo. Libonisa ukuba sum of the amanani kodwa enye nkqo yaye tye. Magic square "obuqhelekileyo" kuphela xa kuthe ekwakufudula bazalise amanani zendalo ubunye.

Kunjalo kukho into enjalo njenge sikwere twatsa magic - oku xa ixabiso Isiphumo samanani amabini ilingana, ngexesha xa zicwangciswe symmetrically ngokuphathelele kweli ziko.

Kwakhona kubalulekile ukwazi ukuba zembutho unokuba nayiphi ubukhulu ukongeza ukuya 2 2 isikwere 1 1 kwakhona kucingelwa ukuba zobugqi, njengoko izalisekile zonke iimeko, nangona iquka nenombolo eyodwa.

Ngoko ke, le nkcazelo siye sifunde, ngoku makhe sithethe yokusombulula njani isikwere ngomlingo. 3 iklasi ikharityhulam akunakwenzeka ukuba uchaze yonke into njengoko kuchaziwe njengoko eli nqaku.

Zeziphi izisombululo

Abo bantu abazi ukuba yokusombulula isikwere magic (3 iklasi uyazi kakuhle), ngoko nangoko ukuba izisombululo ezithathu kuphela, yaye ngamnye kubo efanelekileyo izikwere ezahlukeneyo, kodwa ayikwazi ngoyaba isisombululo yesine, oko kukuthi, i "random" . Ngapha koko, ngandlel 'ithile kukho kungenzeka ukuba abantu ningazi kuba nako ukusombulula le puzzle. Kodwa le ndlela sibekela bucala kwibhokisi elide uye ngqo fomyula kunye nobuchule.

Indlela yokuqala. Xa sigcawu limnqakathi

Le ndlela efanelekileyo kuphela ukusombulula isikwere, nethe inani elingumnqakathi leeseli, umzekelo, i-3 ngo-3 okanye 5 kwi-5.

Ngoko ke, kulo naliphi na ityala kuqala kufuneka ufumane rhoqo omlingo. Eli nani, efunyanwa xa isixa amanani idiagonally, nkqo yaye tye. Oku kubalwa usebenzisa ifomula:

Kulo mzekelo, siqwalasela isikwere ezintathu bathathu, ifomula wayeza khangela ngathi kunjalo (n - inani columns):

Ngoko ke, siya kuba isikwere. Into yokuqala ukuyenza - ukuba ufake inombolo enye embindini kumgca wokuqala ukusuka phezulu. Onke amanani ezilandelayo kufuneka zibekwe kwimigaqo ebuhlanti enye kwi idiagonal.

Kodwa ngoko nangoko umbuzo othi, ukuyisombulula njani isikwere magic? Grade 3 akunakwenzeka ukuba ukusebenzisa le ndlela, kwaye uninzi iya kuba yingxaki, indlela ukuyenza ngale ndlela; ukuba oku na iseli? Ukwenza izinto, kufuneka usebenzise ngqondweni wakho nilwenze isikwere efanayo magic phezulu kwaye icace phandle ukuba inani 2 uya kubakho kulo esiseleni asezantsi ekunene. Ngenxa yoko, kwi square lethu singena ezimbini kwindawo enye. Oku kuthetha ukuba kufuneka ukuba ufake iinombolo ukuze sonke ke banika ixabiso le-15.

amanani elandelayo ulunga ngendlela efanayo. Leyo-3 iza kuba embindini kwikholam yokuqala. Kodwa 4 Akuyi kuba nako ukubhala ngalo mgaqo, ekubeni indawo yayo sele iyunithi. Kulo mzekelo, inani 4 ibekwe phantsi 3, uze uqhubeke. Emihlanu - embindini lisisikweri, 6 - kwikona ephezulu ngasekunene, 7 - 6, 8 - kwesokunxele eliphezulu 9 - embindini umgca osezantsi.

Ngoku uyazi indlela yokucombulula isikwere ngomlingo. Demidov wenza iklasi 3, kodwa ke lo mbhali yaba umsebenzi kancinane lula, kodwa ukwazi indlela ukuze bakwazi ukucombulula naziphi na iingxaki ezinjalo. Kodwa ke oku, ukuba oyinqaba inani columns. Noko ukwenza ntoni, ukuba thina, umzekelo, isikwere 4 4? Oku ngakumbi kwi kwisicatshulwa.

Indlela yesibini. Ukuze inxaki lo ukulingana kabini

Square kabini-zixatyiswe ekuthiwa kunye nenani lwemihlathi enokwahlulwa no-2, kunye 4. Ngoku sicinga isikwere 4 4.

Ngoko ke, indlela yokusombulula isikwere magic (Grade 3, Demidov, Kozlov, zingcakacile - ukuseta kwi textbook yemathematika), xa inani lwemihlathi yakhe ilingana no-4? Yinto elula kakhulu. Lula ngakumbi umzekelo ngaphambili.

Kwindawo yokuqala sifumana rhoqo magic usebenzisa ifomula efanayo wavalelwa ngexesha lokugqibela. Kulo mzekelo, inani 34 Ngoku kufuneka sakhele amanani ezinjalo ukuba udibaniso nkqo, tye kunye nemigca elinganayo iyafana.

Okokuqala kufuneka ukupeyinta ezinye iiseli ukwenza oku, wena ungakwazi ipensile okanye ngobungqola. Peyinta phezu zonke engile, oko kukuthi, iseli ephezulu ekhohlo ne ekunene ephezulu, asezantsi yasekhohlo kunye esekunene ezantsi. Ukuba isikwere bekuya kuba 8 ngu 8, ngoko ke akukho mfuneko yokuba ukupeyinta kwibhokisi enye kwikona, yaye ezine, yokulinganisa 2 ngu-2.

Ngoku kufuneka ukupeyinta embindini isikwere, kangangokuba engile saso ezimbombeni zaso ezichaphazelekayo iiseli esele mnyama. Kulo mzekelo, sifumana isikwere embindini 2 ngu-2.

Ukufumana ukugcwaliswa. Kuyizalisa ukusuka ekhohlo ukuya ekunene kwi indlela apho indawo iiseli, ngenisa nje ixabiso iya kuba iiseli mnyama. Kubonakala ukuba ikona yasekhohlo ephezulu 1 wangena kwi ekunene - 4. Emva koko bhala engundoqo 6, 7, yaye ngakumbi 10 no 11. ekhohlo ophantsi nasekunene 13 - 16. Siyakholwa inkqubo yokuzaliswa ecacileyo.

Iiseli aseleyo zizaliswe ngendlela efanayo, kuphela eyehlayo. Oku kungenxa yokuba yokugqibela sele ebhaliwe mfanekiso-16, encotsheni isikwere ukubhala 15. Eminye 14 12, 9 njalo njalo, njengoko kubonisiwe emfanekisweni.

Ngoku uyazi indlela yesibini ukusombulula isikwere ngomlingo. Grade 3 uyavuma ukuba isikwere of kabini-zixatyiswe kulula kakhulu ukusombulula ngaphezu kwabanye. Kulungile, sibheka kuzo indlela yokugqibela.

Indlela yesithathu. Ukuze phinda inxaki ethile ukulingana eyodwa

ubo eyodwa Square kuthiwa isikweri inani lwemihlathi ukuba zingahlulwa zibe mbini, kodwa abane. Kulo mzekelo, kwisikweri ka 6 6.

Ngoko ke, thina ubale rhoqo omlingo. Kuyinto ilingana 111.

Ngoku kufuneka ukuba inxaki abangaboniyo yahlulwe isikwere ezine ezahlukeneyo-3 ngo 3. 3 babe ubukhulu ezine encinane yembutho 3 enye enkulu 6 6. Upper ekhohlo kuthiwa A, i asezantsi ekunene - B, ilungelo eliphezulu - esezantsi ekhohlo kwaye C - D.

Ngoku ke kufuneka ukuba ukusombulula isikwere ngalinye elincinane, usebenzisa indlela yokuqala olufumaneka kweli nqaku. Kungcono ninikane ukuze isikwere A iinombolo ukusuka ku-1 ukuya kwi-9, kwi-V - ukususela-10 ukuya kwi-18, C - nge-19 ukuya 27 no D - 28 ukuya ku-36.

Wakuba wenze isigqibo zonke izikwere ezine, umsebenzi ziya kuqalisa A no D. Kufuneka kwi square A abangaboniyo okanye ipensile yahlulwe iiseli ezintathu, ezizezi, ephezulu ekhohlo, asezantsi ngasekhohlo, kunye neziko. Out ukuze iinamba abelwe - ngu 8, 5 kunye 4. Ngokufanayo, kuyimfuneko ukuchonga kunye Square D (35, 33, 31). Konke oko uhlala ukwenza i swap amanani abelwe ye square D ku A.

Ngoku uyazi indlela yokugqibela indlela unokuyilungisa isikwere ngomlingo. Grade 3 ubo enye square akamthandi kakhulu. Akumangalisi oku, kuba konke Wawusondeza zinzima.

isiphelo

Emva kokufunda eli nqaku, eli cebiso ukuze nisombulule njani isikwere ngomlingo. Grade 3 (Moreau - nombhali textbook) unika imisebenzi efanayo kunye iiseli nje ezimbalwa kuhluthiswa. Cinga nje ngomzekelo wakhe akwenzi ngqiqo, njengokuba ukwazi zonke zontathu ndlela, unako ngokulula ukusombulula zonke iinjongo ecetywayo.