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‡Kv‡bv m~PK GKvwaK msL¨v wewkó n‡q _vK‡jI GwU mivmwi K¨vjKz‡jU‡i cÖ‡ek Kiv‡bv hvq| D`vniY¯^iƒc, wb‡Pi
cÖ_g w¯Œ‡bi w`‡K fv‡jv K‡i jÿ¨ Ki‡j †`Lv hv‡e †h, 11 Gi NvZ 3 + 4.
K¨vjKz‡jU‡i m~PKxq MYbv Kivi Rb¨ $ Kx e¨envi K‡i wfwË ‡_‡K Nv‡Z Ges cybvivq NvZ †_‡K wfwˇZ wM‡q
3
ivwkwU UvBc Ki‡Z n‡e| Dc‡i jÿ¨ Ki‡j †`Lv hv‡e †h, 11 3+4 I 11 + 4 ivwk `ywU m¤ú~Y© Avjv`v| cÖ_g
3
ivwk‡Z 4 m~P‡Ki mv‡_ †hvM Kiv n‡q‡Q| Avi wØZxq ivwk‡Z 4,11 Gi mv‡_ †hvM Kiv n‡q‡Q|
cÖ_g ivwkwUi A_© n‡jv 11 × 11 × 11 × 11 × 11 × 11 × 11 †hLv‡b wØZxq ivwkwUi A_© n‡jv 11 ×
11 × 11 + 4 †h¸‡jv Aek¨B GKwU AciwU †_‡K Avjv`v|
2
‡Kv‡bv NvZ wewkó msL¨vi Dci NvZ _vK‡j Zv K¨vjKz‡jU‡i mivmwi †ei Kiv hvq| D`vniY¯^iƒc aiv hvK, 4 Gi
2
2
2 3
2
wZbZg NvZ n‡jv 4 × 4 × 4 hv (4 ) Gfv‡e wjLv hvq | Aek¨B mZK©Zvi m‡½ eÜbx cÖ‡ek Kiv‡Z n‡e
Ges cieZ©x NvZ cÖ‡ek Kiv‡bvi Rb¨ $ evUb e¨envi Ki‡Z n‡e| GwU wb‡P †`Lv‡bv n‡jv-
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cÖvß djvdjwU 4 Gi gv‡bi mgvb| †Kbbv NvZ¸‡jv †hvM Ki‡j cvIqv hvq 2 + 2 + 2 = 6| AviI jÿYxq
2 3
3 2
†h 2 + 2 + 2 = 3 × 2 = 6. AviI †`Lv hvq †h (4 ) I (4 ) GKB djvdj †`q †Kbbv 2 × 3 = 3 ×
2 = 6| hw` eª¨v‡KU bv †`qv nq Zvn‡j K¨vjKz‡jUi †k‡li NvZwU‡K Zvi c~‡e©i msL¨vi NvZ wn‡m‡e we‡ePbv
3
Ki‡e| ZvB wb‡Pi ivwkwU hv ^ Kx cici `yB evi e¨envi K‡i cvIqv †M‡Q Zvi gvb n‡e 4 Gi 2 ev 8 Zg
NvZ Gi gvb|
hw`I me mgq ^ evUb e¨envi K‡i NvZ †ei Kiv hvq, wKš‘ wØNv‡Zi Rb¨ devUb I wÎNv‡Zi Rb¨
3
qd( ) evUb e¨envi Kiv AwaK myweavRbK| GB wb‡`©kbv¸‡jvI NvZ evUb ^ Gi g‡Zv GKB djvdj
†`q| (hw`I K¨vjKz‡jUi Zv‡`i GKUz wfbœ fv‡e MYbv K‡i)|
†ÿÎdj wbY©q Ki‡Zd evUb mivmwi e¨envi Kiv hvq| wb‡Pi w¯Œ‡b 8 e¨vmva© wewkó e„‡Ëi †ÿÎdj mivmwi
†ei Kiv n‡q‡Q| wb‡Pi w¯Œ‡b qK‡P‡c e¨envi Kiv n‡q‡Q|
7