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 Crossnumber II (Posted on 2013-05-27)
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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 helpful table | Comment 1 of 2
` n   n^2 n^2 (Roman) Length of Roman                      representation 1     1 I                 110   100 C                 1`
` 2     4 IV                2 3     9 IX                220   400 CD                230   900 CM                2`
` 4    16 XVI               3 5    25 XXV               340  1600 MDC               350  2500 MMD               3`
` 7    49 XLIX              4 8    64 LXIV              411   121 CXXI              4`
` 6    36 XXXVI             5 9    81 LXXXI             512   144 CXLIV             513   169 CLXIX             514   196 CXCVI             515   225 CCXXV             516   256 CCLVI             521   441 CDXLI             523   529 DXXIX             525   625 DCXXV             531   961 CMLXI             532  1024 MXXIV             534  1156 MCLVI             539  1521 MDXXI             545  2025 MMXXV             549  2401 MMCDI             551  2601 MMDCI             560  3600 MMMDC             5`
`19   361 CCCLXI            624   576 DLXXVI            635  1225 MCCXXV            646  2116 MMCXVI            647  2209 MMCCIX            655  3025 MMMXXV            6`
`18   324 CCCXXIV           726   676 DCLXXVI           727   729 DCCXXIX           729   841 DCCCXLI           733  1089 MLXXXIX           736  1296 MCCXCVI           738  1444 MCDXLIV           748  2304 MMCCCIV           752  2704 MMDCCIV           754  2916 MMCMXVI           7`
`17   289 CCLXXXIX          822   484 CDLXXXIV          837  1369 MCCCLXIX          841  1681 MDCLXXXI          842  1764 MDCCLXIV          844  1936 MCMXXXVI          853  2809 MMDCCCIX          8`
`28   784 DCCLXXXIV         943  1849 MDCCCXLIX         956  3136 MMMCXXXVI         957  3249 MMMCCXLIX         961  3721 MMMDCCXXI         963  3969 MMMCMLXIX         9`
`58  3364 MMMCCCLXIV       1059  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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