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 One, two, eight etc (Posted on 2015-05-22)
List all the numbers (below 4000) that their Roman numeral representations have the same number of letters as their squares.

 See The Solution Submitted by Ady TZIDON No Rating

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 adding overbars for large squares Comment 2 of 2 |
(In reply to computer solution not considering overlining for large squares by Charlie)

Adding code to allow for overbarred numerals, the list expands considerably.  Fortunately, 1000, either as M or an overbarred I, still is one character so it doesn't affect the count.  In the below, for the squares of 32 - 39, the same numbers appear below in a different manner, but the same character count.  I've put the overbarred letters on the left, followed by a space and then the non-barred letters, but the space doesn't count in the character count. In some cases there is/are only overbarred letters; so if there is no space and the square is over 1000, be assured all the letters should be overbarred, such as X for 10000, the square of 100 (C) or M for 1,000,000, the square of M for 1,000.

`     1        1   I               I     2        4   II              IV     8       64   VIII            LXIV    10      100   X               C    20      400   XX              CD    23      529   XXIII           DXXIX    32     1024   XXXII           I XXIV    34     1156   XXXIV           I CLVI    38     1444   XXXVIII         I CDXLIV    39     1521   XXXIX           I DXXI    71     5041   LXXI            V XLI    80     6400   LXXX            VI CD    84     7056   LXXXIV          VII LVI    98     9604   XCVIII          IX DCIV   100    10000   C               X    148    21904   CXLVIII         XXI CMIV   200    40000   CC              XL    227    51529   CCXXVII         LI DXXIX   230    52900   CCXXX           LII CM   237    56169   CCXXXVII        LVI CLXIX   238    56644   CCXXXVIII       LVI DCXLIV   243    59049   CCXLIII         LIX XLIX   245    60025   CCXLV           LX XXV   246    60516   CCXLVI          LX DXVI   253    64009   CCLIII          LXIV IX   320   102400   CCCXX           CII CD   331   109561   CCCXXXI         CIX DLXI   332   110224   CCCXXXII        CX CCXXIV   338   114244   CCCXXXVIII      CXIV CCXLIV   340   115600   CCCXL           CXV DC   380   144400   CCCLXXX         CXLIV CD   381   145161   CCCLXXXI        CXLV CLXI   389   151321   CCCLXXXIX       CLI CCCXXI   390   152100   CCCXC           CLII C   399   159201   CCCXCIX         CLIX CCI   436   190096   CDXXXVI         CXC XCVI   449   201601   CDXLIX          CCI DCI   638   407044   DCXXXVIII       CDVII XLIV   710   504100   DCCX            DIV C   718   515524   DCCXVIII        DXV DXXIV   742   550564   DCCXLII         DL DLXIV   743   552049   DCCXLIII        DLII XLIX   745   555025   DCCXLV          DLV XXV   747   558009   DCCXLVII        DLVIII IX   775   600625   DCCLXXV         DC DCXXV   782   611524   DCCLXXXII       DCXI DXXIV   800   640000   DCCC            DCXL    831   690561   DCCCXXXI        DCXC DLXI   834   695556   DCCCXXXIV       DCXCV DLVI   838   702244   DCCCXXXVIII     DCCII CCXLIV   840   705600   DCCCXL          DCCV DC   898   806404   DCCCXCVIII      DCCCVI CDIV   980   960400   CMLXXX          CMLX CD   998   996004   CMXCVIII        CMXCVI IV  1000  1000000   M               M   1049  1100401   MXLIX           MC CDI  1227  1505529   MCCXXVII        MDV DXXIX  1245  1550025   MCCXLV          MDL XXV  1248  1557504   MCCXLVIII       MDLVII DIV  1253  1570009   MCCLIII         MDLXX IX  1379  1901641   MCCCLXXIX       MCMI DCXLI  1384  1915456   MCCCLXXXIV      MCMXV CDLVI  1388  1926544   MCCCLXXXVIII    MCMXXVI DXLIV  1397  1951609   MCCCXCVII       MCMLI DCIX  1398  1954404   MCCCXCVIII      MCMLIV CDIV  1416  2005056   MCDXVI          MMV LVI  1468  2155024   MCDLXVIII       MMCLV XXIV  1480  2190400   MCDLXXX         MMCXC CD  1584  2509056   MDLXXXIV        MMDIX LVI  1738  3020644   MDCCXXXVIII     MMMXX DCXLIV  1871  3500641   MDCCCLXXI       MMMD DCXLI  1888  3564544   MDCCCLXXXVII    MMMDLXIV DXLIV  1898  3602404   MDCCCXCVIII     MMMDCII CDIV  `

DefDbl A-Z
Dim crlf\$
Function mform\$(x, t\$)
a\$ = Format\$(x, t\$)
If Len(a\$) < Len(t\$) Then a\$ = Space\$(Len(t\$) - Len(a\$)) & a\$
mform\$ = a\$
End Function
pad\$ = Left(x + Space\$(l), l)
End Function

Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

For i = 1 To 4000
rm\$ = roman(i)
l = Len(rm\$)
sq = i * i
If sq > 1000 Then
pt1 = sq \ 1000: pt2 = sq Mod 1000
pt1r\$ = roman(pt1): pt2r\$ = roman(pt2)
l2 = Len(pt1r + pt2r)
rmsq\$ = pt1r + " " + pt2r
Else
l2 = Len(roman(sq))
rmsq\$ = roman(sq)
End If
If l = l2 Then
Text1.Text = Text1.Text & mform(i, "#####0") & mform(i * i, "########0") & "   "
Text1.Text = Text1.Text & pad(rm\$, 12) & "    " & rmsq & crlf
End If
DoEvents
Next

Text1.Text = Text1.Text & "done" & crlf
End Sub

Function roman\$(n)
q = n \ 1000: r = n Mod 1000
ro\$ = String\$(q, "M")
n2 = r
q = n2 \ 100: r = n2 Mod 100
Select Case q
Case 9: ro\$ = ro\$ + "CM"
Case 5 To 8: ro\$ = ro\$ + "D" + String\$(q - 5, "C")
Case 4: ro\$ = ro\$ + "CD"
Case 0 To 3: ro\$ = ro\$ + String\$(q, "C")
End Select
n2 = r
q = n2 \ 10: r = n2 Mod 10
Select Case q
Case 9: ro\$ = ro\$ + "XC"
Case 5 To 8: ro\$ = ro\$ + "L" + String\$(q - 5, "X")
Case 4: ro\$ = ro\$ + "XL"
Case 0 To 3: ro\$ = ro\$ + String\$(q, "X")
End Select
n2 = r
q = n2
Select Case q
Case 9: ro\$ = ro\$ + "IX"
Case 5 To 8: ro\$ = ro\$ + "V" + String\$(q - 5, "I")
Case 4: ro\$ = ro\$ + "IV"
Case 0 To 3: ro\$ = ro\$ + String\$(q, "I")
End Select

roman\$ = ro\$

End Function

 Posted by Charlie on 2015-05-22 13:05:09

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