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 How far can you go? (Posted on 2015-05-12)
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!

 See The Solution Submitted by Ady TZIDON No Rating

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 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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