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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  
8       9          
10   11 12            
13           14 15   16
17         18        

       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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Solution solution Comment 2 of 2 |

The 2-digit squares can begin only with I or C, and no 8-letter square can have an I in either the second or the third position, so 2-down and 3-down each begin with C.

That 8-letter square, 1-across, must then be MCCCLXIX.

The only 4-letter square beginning with X is XLIX, so that must go in 6-down.

The only 5-letter square beginning with X is XXXVI, so that's 5-down.

No 6-letter square has an I in the second position, so the 2-letter 8-across must begin with C. Then 1-down must be a 6-letter square beginning with M and having D or M in the third position. Only MMMXXV fits this.

17-across has three letters, the middle of which is V. Only XVI fits this.

14-across is either IV or IX. Since no 4-letter square begins with V, it must be IX, and 15-down must be XLIX, the only 4-letter square beginning with X.

When C is in the second position of a 6-letter square, then so is the third position, so 10-across begins with a C, and is either CXLIV or CXCVI. But if it were the latter, 11-down would begin with C, which could only be CXXI, conflicting with the already placed I at the end of 17-across. So 10-across is CXLIV, and 11-down is forced to be LXIV.

4-down is CC_VI, which can only be CCLVI.

Then 9-across, L_X_I, can only be LXXXI.

20-across has 7 letters, the second of which must be V, X, D or M, as the second spot for a 2-letter square at 19-down, and whose 5th position already has an X. So 20-across is MMCMXVI.

19-down must be CM and 18-down MDC.

The 4-letter square at 16-down, ending in I, must be CXXI.

The puzzle is then finished.

  M C C C L X I X
M M M D C   X   L
C M     L X X X I
C X L I V   V   X
X X X V I   I X   C
X V I     M   L   X
V   V   C D   I   X
      M M C M X V I

  Posted by Charlie on 2013-05-27 14:13:27
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