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

 Square and Consecutive Settlement (Posted on 2010-09-10)
Determine the probability that for a base 11 perfect square P chosen at random between 1,000,000,000 (base 11) and A,AAA,AAA,AAA (base 11) inclusively, the five digit number formed by the last five digits of P (reading left to right) is precisely one more than the number formed by the first five digits.

 See The Solution Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution Comment 1 of 1
`list   10   dim Dig(10)   20   Strt=-int(-sqrt(11^9))   30   Fin=int(sqrt(11^10-1))   40   for Root=Strt to Fin   50      Sq=Root*Root   60      for I=0 to 9   70         Dig(I)=Sq @ 11   80         Sq=Sq\11   90      next I  100      N1=0  110      for I=9 to 5 step -1  120         N1=N1*11+Dig(I)  130      next I  140      N2=0  150      for I=4 to 0 step -1  160         N2=N2*11+Dig(I)  170      next I  180      if N2=N1+1 then print Root*Root  185        :for I=9 to 0 step -1:print Dig(I);:if I=5 then print "   ";:endif  186        :next:print  190   next Root  200   print:print Fin-Strt+1OKrun 2881864489 1  2  4  9  8     1  2  4  9  9 6484275625 2  8  2  8  2     2  8  2  8  3 6484597729 2  8  2  8  4     2  8  2  8  5 11528102161 4  9  8  6  3     4  9  8  6  4 18012055681 7  7  0  3  3     7  7  0  3  4`
` 112492OK`

shows that 5 of the 112,492 perfect squares in the given range satisfy the condition, so the probability is 5/112,492.

The table printed shows the decimal representation of the square, followed by the base-11 representation. The middle of the latter is spaced farther than the other digits to highlight the two separate parts asked for by the puzzle.

 Posted by Charlie on 2010-09-10 14:16:29
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 (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information