Menu Close

hi-masters-look-at-this-thing-carefully-1-2-3-4-5-6-7-8-9-




Question Number 141087 by greg_ed last updated on 15/May/21
hi, masters !  look at this thing carefully :                                                  1                                              2 3 4                                          5 6 7 8 9                             10 11 12 13 14 15 16                         17 18 19 20 .................     find the line and the column where the number 795471 will appear !
$$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{masters}}\:! \\ $$$$\boldsymbol{\mathrm{look}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{thing}}\:\boldsymbol{\mathrm{carefully}}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\:\mathrm{3}\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{6}\:\mathrm{7}\:\mathrm{8}\:\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{10}\:\mathrm{11}\:\mathrm{12}\:\mathrm{13}\:\mathrm{14}\:\mathrm{15}\:\mathrm{16} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{17}\:\mathrm{18}\:\mathrm{19}\:\mathrm{20}\:…………….. \\ $$$$\:\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{line}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{column}}\:\boldsymbol{\mathrm{where}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\mathrm{795471}\:\boldsymbol{\mathrm{will}}\:\boldsymbol{\mathrm{appear}}\:! \\ $$
Answered by talminator2856791 last updated on 08/Sep/21
    ⌈(√(795471)) ⌉ = ⌈ 891.89181 ⌉ = 892   892 is the line   795471 − 891^2  = 1590   1590th column counting from most left
$$\: \\ $$$$\:\lceil\sqrt{\mathrm{795471}}\:\rceil\:=\:\lceil\:\mathrm{891}.\mathrm{89181}\:\rceil\:=\:\mathrm{892} \\ $$$$\:\mathrm{892}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line} \\ $$$$\:\mathrm{795471}\:−\:\mathrm{891}^{\mathrm{2}} \:=\:\mathrm{1590} \\ $$$$\:\mathrm{1590th}\:\mathrm{column}\:\mathrm{counting}\:\mathrm{from}\:\mathrm{most}\:\mathrm{left}\: \\ $$$$\: \\ $$
Answered by qaz last updated on 15/May/21
  1,3,7,13,21,...                       1...1......1      2  4  6  8                                  2...3......3         2   2  2                                   3...7......5                                                         4...13....7                                                          ............                                                         n...a_n ....Tn  S_n = ((n),(1) )+2 ((n),(2) )+2 ((n),(3) )   a_n =S_n −S_(n−1) =n^2 −n+1  795471=n^2 −n+1    ⇒l=n≈892  If n=892,number 794773 is at [l:892,c:892]  795471−794773=698  So 795471 is at [l:892,c:1590]
$$\:\:\mathrm{1},\mathrm{3},\mathrm{7},\mathrm{13},\mathrm{21},…\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}…\mathrm{1}……\mathrm{1} \\ $$$$\:\:\:\:\mathrm{2}\:\:\mathrm{4}\:\:\mathrm{6}\:\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}…\mathrm{3}……\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\mathrm{2}\:\:\:\mathrm{2}\:\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}…\mathrm{7}……\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}…\mathrm{13}….\mathrm{7} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{n}…{a}_{{n}} ….{Tn} \\ $$$${S}_{{n}} =\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}+\mathrm{2}\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}+\mathrm{2}\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\: \\ $$$${a}_{{n}} ={S}_{{n}} −{S}_{{n}−\mathrm{1}} ={n}^{\mathrm{2}} −{n}+\mathrm{1} \\ $$$$\mathrm{795471}={n}^{\mathrm{2}} −{n}+\mathrm{1}\:\:\:\:\Rightarrow{l}={n}\approx\mathrm{892} \\ $$$${If}\:{n}=\mathrm{892},{number}\:\mathrm{794773}\:{is}\:{at}\:\left[{l}:\mathrm{892},{c}:\mathrm{892}\right] \\ $$$$\mathrm{795471}−\mathrm{794773}=\mathrm{698} \\ $$$${So}\:\mathrm{795471}\:{is}\:{at}\:\left[{l}:\mathrm{892},{c}:\mathrm{1590}\right] \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *