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How far can you go? (Posted on 2015-05-12) Difficulty: 2 of 5
16 is the smallest 2-digit square whose digits are non-decreasing.
144 is the smallest 3-digit square whose digits are non-decreasing.
1156 is the smallest 4-digit square whose digits are non-decreasing.

GO ON!

No Solution Yet Submitted by Ady TZIDON    
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Solution computer exploration | Comment 3 of 6 |
The squares and their square roots:

 16   4 
 144   12 
 1156   34 
 11236   106 
 111556   334 
 2666689   1633 
 11115556   3334 
 277788889   16667 
 1111155556   33334 
 11122233444   105462 
 111111555556   333334 
 2777778888889   1666667 
 11111115555556   3333334 
 277777788888889   16666667 
 1111111155555556   33333334 
 27777777888888889   166666667 
 111111111555555556   333333334 
 2777777778888888889   1666666667 
 11111111115555555556   3333333334 
 
 (stopped as the rest take "forever")
 
 
  5   open "howfargo.txt" for output as #2
 10   Base=11
 20   loop
 30      Sr=-int(-sqrt(Base))
 40      Good=0
 50      while Good=0
 60        Sq=Sr*Sr
 70        S$=cutspc(str(Sq))
 75        Good=1
 80        for I=2 to len(S$)
 90           if mid(S$,I,1)<mid(S$,I-1,1) then Good=0:cancel for:goto 120
100        next
120        if Good=0 then inc Sr
130      wend
140      print Sq,Sr:print #2,Sq,Sr
150      Base=Base*10+1
160   endloop


  Posted by Charlie on 2015-05-12 10:26:36
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