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Crossnumber II (Posted on 2013-05-27) Difficulty: 4 of 5
This cross-number uses Roman numbers only and, every clue is the same. (Examples of five Roman numbers are VIII = 8, LXXVI = 76, CXXXVI = 136, CM = 900 and MDCCCLXII = 1862.)

  1 2 3 4   5   6  
7                  
8       9          
10   11 12            
13           14 15   16
17         18        
        19          
      20            
                                                               

       ACROSS                                DOWN

 1. A perfect square                     1. A perfect square           
 7. A perfect square                     2. A perfect square           
 8. A perfect square                     3. A perfect square         
 9. A perfect square                     4. A perfect square           
10. A perfect square                     5. A perfect square   
13. A perfect square                     6. A perfect square 
14. A perfect square                     7. A perfect square       
17. A perfect square                    11. A perfect square         
19. A perfect square                    12. A perfect square          
20. A perfect square                    15. A perfect square         
                                        16. A perfect square
                                        18. A perfect square
                                        19. A perfect square

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Hints/Tips helpful table | Comment 1 of 2
 n   n^2 n^2 (Roman) Length of Roman
                      representation
 1     1 I                 1
10   100 C                 1
 2     4 IV                2
 3     9 IX                2
20   400 CD                2
30   900 CM                2
 4    16 XVI               3
 5    25 XXV               3
40  1600 MDC               3
50  2500 MMD               3
 7    49 XLIX              4
 8    64 LXIV              4
11   121 CXXI              4
 6    36 XXXVI             5
 9    81 LXXXI             5
12   144 CXLIV             5
13   169 CLXIX             5
14   196 CXCVI             5
15   225 CCXXV             5
16   256 CCLVI             5
21   441 CDXLI             5
23   529 DXXIX             5
25   625 DCXXV             5
31   961 CMLXI             5
32  1024 MXXIV             5
34  1156 MCLVI             5
39  1521 MDXXI             5
45  2025 MMXXV             5
49  2401 MMCDI             5
51  2601 MMDCI             5
60  3600 MMMDC             5
19   361 CCCLXI            6
24   576 DLXXVI            6
35  1225 MCCXXV            6
46  2116 MMCXVI            6
47  2209 MMCCIX            6
55  3025 MMMXXV            6
18   324 CCCXXIV           7
26   676 DCLXXVI           7
27   729 DCCXXIX           7
29   841 DCCCXLI           7
33  1089 MLXXXIX           7
36  1296 MCCXCVI           7
38  1444 MCDXLIV           7
48  2304 MMCCCIV           7
52  2704 MMDCCIV           7
54  2916 MMCMXVI           7
17   289 CCLXXXIX          8
22   484 CDLXXXIV          8
37  1369 MCCCLXIX          8
41  1681 MDCLXXXI          8
42  1764 MDCCLXIV          8
44  1936 MCMXXXVI          8
53  2809 MMDCCCIX          8
28   784 DCCLXXXIV         9
43  1849 MDCCCXLIX         9
56  3136 MMMCXXXVI         9
57  3249 MMMCCXLIX         9
61  3721 MMMDCCXXI         9
63  3969 MMMCMLXIX         9
58  3364 MMMCCCLXIV       10
59  3481 MMMCDLXXXI       10
62  3844 MMMDCCCXLIV      11

is the output of the following program, sorted on length of representation (major) and n (minor), with heading and blank lines between lengths added manually:

OPEN "crossnm2.txt" FOR OUTPUT AS #2
FOR sr = 1 TO 63
  n = sr * sr
  q = n \ 1000: r = n MOD 1000
  r$ = STRING$(q, "M")
  n2 = r
  q = n2 \ 100: r = n2 MOD 100
  SELECT CASE q
     CASE 9: r$ = r$ + "CM"
     CASE 5 TO 8: r$ = r$ + "D" + STRING$(q - 5, "C")
     CASE 4: r$ = r$ + "CD"
     CASE 0 TO 3: r$ = r$ + STRING$(q, "C")
  END SELECT
  n2 = r
  q = n2 \ 10: r = n2 MOD 10
  SELECT CASE q
     CASE 9: r$ = r$ + "XC"
     CASE 5 TO 8: r$ = r$ + "L" + STRING$(q - 5, "X")
     CASE 4: r$ = r$ + "XL"
     CASE 0 TO 3: r$ = r$ + STRING$(q, "X")
  END SELECT
  n2 = r
  q = n2
  SELECT CASE q
     CASE 9: r$ = r$ + "IX"
     CASE 5 TO 8: r$ = r$ + "V" + STRING$(q - 5, "I")
     CASE 4: r$ = r$ + "IV"
     CASE 0 TO 3: r$ = r$ + STRING$(q, "I")
  END SELECT
  PRINT USING "## ##### \              \ ##"; sr; n; r$; LEN(r$)
  PRINT #2, USING "## ##### \              \ ##"; sr; n; r$; LEN(r$)
NEXT sr


 


  Posted by Charlie on 2013-05-27 11:01:48
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