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

 Subtract 1 from squared abbbb (Posted on 2008-08-16)
Determine all possible five digit positive decimal (base 10) integer(s) of the form abbbb, with a ≠ b, that contain no leading zeroes, such that (abbbb2 - 1) is equal to a positive ten digit integer (with no leading zeroes) containing each of the digits 0 to 9 exactly once.

Note: While the solution may be trivial with the aid of a computer program, show how to derive it without one.

 See The Solution Submitted by K Sengupta Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Yes, it's trivial with a computer program | Comment 4 of 6 |
`  100   for A=1 to 9  200     for B=0 to 9  300       if A<>B then  400         :Tst=10000*A+1111*B:tst1=tst  500         :Tst=Tst*Tst-1  600         :Tsts=cutlspc(str(Tst))  700         :if len(Tsts)=10 then  800           :Good=1  900           :for I=1 to 9 1000             :if instr(mid(Tsts,I+1,*),mid(Tsts,I,1)) then Good=0:endif 1100           :next 1200           :if Good then print Tst1,tst 1300     next B 1400   next A`

giving

85555   7319658024
97777   9560341728

 Posted by Charlie on 2008-08-17 13:35:13

 Search: Search body:
Forums (0)