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yksd foÙk




                  uksV          ekuk rhu djnkrk A, B vkSj C gSa ftuls ljdkj 8 #i;s dj osQ :i esa olwy djuk pkgrh gSA eku yhft;s
                                buesa esa fdlh ,d dks #i;k nsuk iM+rk gS rks fuEu R;kx djuk iM+rk gSµ

                                   #i;ksa dh bdkb;k¡      A }kjk fd;k       B }kjk fd;k        C }kjk fd;k
                                                        x;k lhekUr R;kx    x;k lhekUr R;kx   x;k lhekUr R;kx

                                          1                   15                 20                42
                                          2                   25                 30                51

                                          3                   38                 42                60
                                          4                   42                 50                65

                                          5                   50                 58                69

                                bl fLFkfr esa le&lhekUr R;kx 4 bdkbZ gSA vr% ljdkj ;fn 8 #i;s dj osQ :i esa olwy djuk pkgrh gS rks
                                A ls 4 #i;s] B ls 3 #i;s C ls 1 #i;k olwy djsxhA
                                bl fLFkfr dks js[kkfp=k&4 }kjk vklkuh ls Li"V fd;k tk ldrk gSA ;gk¡ x-v{k rFkk y-v{k ij Øe'k% dj
                                dh ek=kk ,oa dj pqdkus ls R;kx ekik x;k gSA AA  rFkk BB  Øe'k% A ,oa B djnkrk osQ R;kx dks iznf'kZr
                                                                             1
                                                                     1
                                djrs gSa tks ;g crkrs gSa fd tSls&tSls dj dh ek=kk c<+rh tk;sxh oSls&oSls R;kx c<+rk tk;sxkA oqQy R;kx rc
                                U;wure gksxk tc A ,oa B dk lhekUr R;kx cjkcj gksA ;g rHkh lEHko gks ldrk gS tc ljdkj A ls OQ 1
                                rFkk B ls OQ  dj dh ek=kk ,df=kr djs D;ksafd bl fLFkfr esa gh A dk lhekUr R;kx Q M rFkk B dk lhekUr
                                          2                                                    1
                                R;kx Q N cjkcj gSA
                                     2
                                                                           A
                                                             Y              1
                                                                              B

                                                                     M
                                                              L            N

                                                             A
                                                             B
                                                              O       Q   Q     X
                                                                        1  2

                                                                     fp=k 4
                                lekurk ykus osQ fy,] ;g gksuk pkfg, fd /uh O;fDr;ksa ij dj yxk;s tk,¡ vkSj buls gksus okyh izkfIr;k¡ esa
                                ls NksVh vk; okys yksxksa dks ml le; rd vf/nku (bounties) fn;s tk,¡] tc rd fd lekurk dk pje Lrj
                                (dead level) u izkIr dj fy;k tk;sA ijUrq ;fn jkT; ,slk ugha djrk gS rks jktLo dk laxzg iw.kZr;k loksZPp
                                vk; okys oxks± ls fd;k tkuk pkfg,A ljdkj dks pkfg, fd og fuEu vk; okys oxks± dks ml le; rd u Nq,]
                                tc rd fd mPp vk; okys oxZ fuEu vk; okys oxks± osQ Lrj rd u vk;saA bldk vFkZ ;g gS fd dj lcls
                                igys ,sls O;fDr ij yxk;s tkus pkfg, ftldh vk; lokZf/d gks vkSj og blfy, D;ksafd dj yxus ij mls
                                U;wure R;kx djuk gksxkA bl izdkj] djk/ku osQ }kjk tc mldh vk; ?kVdj lekt osQ nwljs lcls cM+s /uh
                                O;fDr osQ Lrj rd vk tk,] rks vc bu nksuksa ij gh dj yxkuk vkjEHk dj nsuk pkfg, vkSj og blfy, D;ksafd
                                tc bu nksuksa osQ }kjk gh dj osQ :i esa vfUre #i;s dh vnk;xh osQ dkj.k tks R;kx fd;k tk;sxk] og cjkcj
                                gksxkA bl izdkj] vc bu nksuksa ij gh dj yxkrs&yxkrs bUgsa lekt osQ rhljs lcls cM+s /uh O;fDr osQ Lrj rd




                                           LOVELY PROFESSIONAL UNIVERSITY
          88                               LOVELY PROFESSIONAL UNIVERSITY
                                           LOVELY PROFESSIONAL UNIVERSITY
                                           LOVELY PROFESSIONAL UNIVERSITY
                                           LOVELY PROFESSIONAL UNIVERSITY
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