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overridetlistid2063752493tlistoverridecount0tls2SIt
listoverridetlistid1311052988tlistoverridecount0tls
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tls4SItlistoverridetlistid1871140750tlistoverrideco
unt0tls5SSItinfoIttitle Constructia unui patrat magic imparSItauthor Raluca Musaloiu-ElefteriSItoperator Raluca Musaloiu-ElefteriSItcreatimtyr1999tmo7tdy8thr17tmi
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ctdefaultcl Itfooter tpardtplain ts17tqctnoidctlpartidctlpartbrdrttbrdrstbrdr5tbrsp
20 ttqcttx4153ttqrttx8306tadjustright tfs20tlang1048tcgrid I- SItfieldIttfldinst Itcs18 PAGE SSItfldrslt Itcs18tlang1024 1SSSItcs18 SItfieldIttfldinst Itcs18 NUMPAGES SSItfldrslt Itcs18tlang1024 1SSSItcs18 -SItpar SSIttpnseclvl1tpnucrmtpnstart1tpnindent720tpnhangI
tpntxta .SSIttpnseclvl2tpnucltrtpnstart1tpnindent720tpnhan
gItpntxta .SSIttpnseclvl3tpndectpnstart1tpnindent720tpnhangI
tpntxta .SSIttpnseclvl4tpnlcltrtpnstart1tpnindent720tpnhan
gItpntxta SSIttpnseclvl5tpndectpnstart1tpnindent720tpnhangIt
pntxtb SItpntxta SSIttpnseclvl6tpnlcltrtpnstart1tpnindent720tpnhang
Itpntxtb SItpntxta SSIttpnseclvl7tpnlcrmtpnstart1tpnindent720tpnhangI
tpntxtb SItpntxta SSIttpnseclvl8tpnlcltrtpnstart1tpnindent720tpnhang
Itpntxtb SItpntxta SSIttpnseclvl9tpnlcrmtpnstart1tpnindent720tpnhangI
tpntxtb SItpntxta SStpardtplain ts15tqctnoidctlpartidctlpartadjustright tf2tfs20tlang1048tcgrid Itf0tfs32 ConstrucSItf71tfs32 tfeSItf0tfs32 ia unui pSItf71tfs32 te3SItf0tfs32 trat magic impartpar Stpard ts15tnoidctlpartidctlpartadjustright Itpar Problematpar Stpardtplain tnoidctlpartidctlpartadjustright tfs20tlang1048tcgrid Itpar Stpardtplain ts15tqjtnoidctlpartidctlpartadjustright tf2tfs20tlang1048tcgrid Itf71 ttab Ste3 se construiascte3 un pte3trat magic de dimensiune n cu n impar, adicte3 o matrice cu n linii si n coloane avte2nd ca elemente numerele naturale 1, 2, ..., n2 astfel teencte2t sumele elementelor pe linii, pe colSItf0 oane si pe cele doua diagonale sa fie identice.tpar Stpard ts15tnoidctlpartidctlpartadjustright Itf0 tpar Stpardtplain ts2tsb240tsa60tkeepntnoidctlpartidctlpartoutlinele
vel1tadjustright tf19tlang1048tcgrid Itf0 Introduceretpar Stpardtplain tqjtnoidctlpartidctlpartadjustright tfs20tlang1048tcgrid Ittab Un SItitf71 pte3trat magicSItf71 constte3 dintr-un tablou de numere aranjate teen forma unui pte3trat, astfel teencte2t sumele elementelor din fiecare linie, coloante3 tbai din cele doute3 diagonale ste3 fie identice valoarea sumei se numetbate SItitf71 numte3r magicSItf71 . Un pte3trat magic este de ordin SIti nSItf71 dacte3 pe o laturte3 a sa sunt atbaezate SIti nSItf71 numere, iar teen componentfea sa intrte3 numerele 1, 2, 3t85, nSItsuper 2SItf71 atunci numte3rul magic poate fi calculat cu formula SItitf71 numte3r magic nnSItitsuper 2SIti 12.SItpar SItfs24 ttab tpar SItf71 ttab Existte3 un singur pte3trat magic de ordinul 3 cu toate cte3 prin rotatfeii tbai simetrii pot fi obtfeinute 8 astfel de pte3tratetpar SItpar Sttrod ttrgaph108ttrleft3119ttrbrdrttbrdrstbrdr15tbrdrcf1 ttrbrdrltbrdrstbrdr15tbrdrcf1 ttrbrdrbtbrdrstbrdr15tbrdrcf1 ttrbrdrrtbrdrstbrdr15tbrdrcf1 ttrbrdrhtbrdrstbrdr15tbrdrcf1 ttrbrdrvtbrdrstbrdr15tbrdrcf1 tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx3576tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx4033tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx4490tpard tqjtnoidctlpartidctlpartintbltadjustright I4tcell 3tcell 8tcell Stpard tnoidctlpartidctlpartintbltadjustright Itro Sttrod ttrgaph108ttrleft3119ttrbrdrttbrdrstbrdr15tbrdrcf1 ttrbrdrltbrdrstbrdr15tbrdrcf1 ttrbrdrbtbrdrstbrdr15tbrdrcf1 ttrbrdrrtbrdrstbrdr15tbrdrcf1 ttrbrdrhtbrdrstbrdr15tbrdrcf1 ttrbrdrvtbrdrstbrdr15tbrdrcf1 tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx3576tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx4033tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx4490tpard tqjtnoidctlpartidctlpartintbltadjustright I9tcell 5tcell 1tcell Stpard tnoidctlpartidctlpartintbltadjustright Itro Sttrod ttrgaph108ttrleft3119ttrbrdrttbrdrstbrdr15tbrdrcf1 ttrbrdrltbrdrstbrdr15tbrdrcf1 ttrbrdrbtbrdrstbrdr15tbrdrcf1 ttrbrdrrtbrdrstbrdr15tbrdrcf1 ttrbrdrhtbrdrstbrdr15tbrdrcf1 ttrbrdrvtbrdrstbrdr15tbrdrcf1 tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx3576tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx4033tclvertalttclbrdrttbrdrstbrdr15tbrdrcf1 tclbrdrltbrdrstbrdr15tbrdrcf1 tclbrdrbtbrdrstbrdr15tbrdrcf1 tclbrdrrtbrdrstbrdr15tbrdrcf1 tcltxlrtb tcellx4490tpard tqjtnoidctlpartidctlpartintbltadjustright I2tcell 7tcell 6tcell Stpard tnoidctlpartidctlpartintbltadjustright Itro Stpard tqjtnoidctlpartidctlpartadjustright Itpar SItf71 ttab Pte3tratele magice de ordin 4 sunt teen numte3r de 880 7040 dacte3 sunt considerate tbai rotatfeiile tbai simetriile, iar numte3rul pte3tratelor magicSIe de ordin 5 este de circa 13.000.000.tpar tpar SItf71 ttab Sunt cunoscute mai multe metode de obtfeinere a pte3tratelor magice, ele diferind pentru pte3tratele de ordin par, respectiv impar.tpar SItpar Stpardtplain ts2tsb240tsa60tkeepntnoidctlpartidctlpartoutlinele
vel1tadjustright tf19tlang1048tcgrid Itf0 Metodatpar Stpardtplain tqjtnoidctlpartidctlpartadjustright tfs20tlang1048tcgrid Itf71 ttab O metodte3 foarte simplte3 constte3 teen urmte3toarele actfeiunitpar Itpntexttpardtplaintf14tfs20tlang1048tcgrid tlochtaf14tdbchtaf0thichtf14 td8ttabSStpard tqjtfi-360tli360tnoidctlpartidctlpartjclisttabttx3
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t360tpnhangItpntxtb td8SStls2tadjustright Itf71 Se plaseazte3 1 teen centrul SIultimei coloanetpar Itpntexttpardtplaintf14tfs20tlang1048tcgrid tlochtaf14tdbchtaf0thichtf14 td8ttabSStpard tqjtfi-360tli360tnoidctlpartidctlpartjc...
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