All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
2011 Square End (Posted on 2011-10-06) Difficulty: 3 of 5
Determine the smallest octal (base 8) perfect square which ends with 2011 (reading left to right). What are the next two smallest octal perfect squares with this property?

***For an extra challenge, solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 1 of 3

 10   Md=8^4
 20   Vl=2*8^3+8+1
 30   for N=1 to 999999
 40    if (N*N) @ Md=Vl then
 50       :print N,N*N,
 60       :Dc=N*N:Rp=""
 70       :while Dc>0
 80         :Rp=cutspc(str(Dc @ 8))+Rp
 90         :Dc=Dc\8
100       :wend
110       :print Rp
120       :Ct=Ct+1:if Ct>40 then end
130   next

Decimal 509^2 = 259,081, which, represented in octal, is 772011, and is the lowest such. The next is  1539^2 = 2368521, which in octal is 11022011. The third is the 30742011 octal seen in the table below.

The decimal representations of such numbers are:

   n      n^2        octal representation of square
 509     259081         772011
 1539    2368521        11022011
 2557    6538249        30742011
 3587    12866569       61052011
 4605    21206025       120712011
 5635    31753225       171102011
 6653    44262409       250662011
 7683    59028489       341132011
 8701    75707401       440632011
 9731    94692361       551162011
 10749   115541001      670602011
 11779   138744841      1021212011
 12797   163763209      1160552011
 13827   191185929      1331242011
 14845   220374025      1510522011
 15875   252015625      1701272011
 16893   285373449      2100472011
 17923   321233929      2311322011
 18941   358761481      2530442011
 19971   398840841      2761352011
 20989   440538121      3220412011
 22019   484836361      3471402011
 23037   530703369      3750362011
 24067   579220489      4241432011
 25085   629257225      4540332011
 26115   681993225      5051462011
 27133   736199689      5370302011
 28163   793154569      5721512011
 29181   851530761      6260252011
 30211   912704521      6631542011
 31229   975250441      7210222011
 32259   1040643081     7601572011
 33277   1107358729     10200172011
 34307   1176970249     10611622011
 35325   1247855625     11230142011
 36355   1321686025     11661652011
 37373   1396741129     12320112011
 38403   1474790409     12771702011
 39421   1554015241     13450062011
 40451   1636283401     14141732011
 41469   1719677961     14640032011
 


The differences between successive values of n (the square roots of the intended numbers) alternate between 1030 and 1018, decimal.
 

 


  Posted by Charlie on 2011-10-06 14:16:03
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information