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USA = n*UK (Posted on 2013-01-21) Difficulty: 2 of 5
Each of the letters in bold represents a base ten digit from 0 to 9 to satisfy these alphametic relationships. None of the numbers can contain any leading zero.
               USA is a multiple of UK, and:
               SA is a multiple of K
Determine the respective minimum and maximum values that USA can assume.

No Solution Yet Submitted by K Sengupta    
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re(3): computer solution - one lower | Comment 4 of 7 |
(In reply to re(2): computer solution - one lower by Charlie)

In fact if leading zeros were allowed (either U or S) then many more solutions would be applicable:

  12           3             12 
  12           4             12
  12           6             12
  14           2             14
  14           7             14
  15           3             15
  16           2             16
  16           4             16
  16           8             16
  18           2             18
  18           3             18
  18           6             18
  18           9             18
  21           3             21
  21           7             21
  23           1             23
  24           1             24
  24           3             24
  24           6             24
  24           8             24
  25           1             25
  26           1             26
  27           1             27
  27           3             27
  27           9             27
  28           1             28
  28           4             28
  28           7             28
  29           1             29
  32           1             32
  32           4             32
  32           8             32
  34           1             34
  34           2             34
  35           1             35
  35           7             35
  36           1             36
  36           2             36
  36           4             36
  36           9             36
  37           1             37
  38           1             38
  38           2             38
  39           1             39
  42           1             42
  42           3             42
  42           6             42
  42           7             42
  43           1             43
  45           1             45
  45           3             45
  45           9             45
  46           1             46
  46           2             46
  47           1             47
  48           1             48
  48           2             48
  48           3             48
  48           6             48
  49           1             49
  49           7             49
  51           3             51
  52           1             52
  52           4             52
  53           1             53
  54           1             54
  54           2             54
  54           3             54
  54           6             54
  54           9             54
  56           1             56
  56           2             56
  56           4             56
  56           7             56
  56           8             56
  57           1             57
  57           3             57
  58           1             58
  58           2             58
  59           1             59
  62           1             62
  63           1             63
  63           7             63
  63           9             63
  64           1             64
  64           2             64
  64           8             64
  65           1             65
  67           1             67
  68           1             68
  68           2             68
  68           4             68
  69           1             69
  69           3             69
  72           1             72
  72           3             72
  72           4             72
  72           6             72
  72           8             72
  72           9             72
  73           1             73
  74           1             74
  74           2             74
  75           1             75
  75           3             75
  76           1             76
  76           2             76
  76           4             76
  78           1             78
  78           2             78
  78           3             78
  78           6             78
  79           1             79
  81           3             81
  81           9             81
  82           1             82
  83           1             83
  84           1             84
  84           2             84
  84           3             84
  84           6             84
  84           7             84
  85           1             85
  86           1             86
  86           2             86
  87           1             87
  87           3             87
  89           1             89
  91           7             91
  92           1             92
  92           4             92
  93           1             93
  94           1             94
  94           2             94
  95           1             95
  96           1             96
  96           2             96
  96           3             96
  96           4             96
  96           8             96
  97           1             97
  98           1             98
  98           2             98
  98           7             98
 104           12            4
 106           12            6
 106           13            6
 108           12            8
 108           14            8
 109           13            9
 203           21            3
 204           21            4
 205           21            5
 206           21            6
 206           23            6
 207           21            7
 208           21            8
 208           24            8
 209           21            9
 209           23            9
 302           31            2
 304           31            4
 304           32            4
 305           31            5
 306           31            6
 306           32            6
 307           31            7
 308           31            8
 308           32            8
 308           34            8
 309           31            9
 402           41            2
 403           41            3
 405           41            5
 406           41            6
 406           42            6
 406           43            6
 407           41            7
 408           41            8
 408           42            8
 409           41            9
 409           43            9
 502           51            2
 503           51            3
 504           51            4
 504           52            4
 506           51            6
 506           52            6
 506           53            6
 507           51            7
 508           51            8
 508           52            8
 508           54            8
 509           51            9
 509           53            9
 602           61            2
 603           61            3
 604           61            4
 604           62            4
 605           61            5
 607           61            7
 608           61            8
 608           62            8
 608           64            8
 609           61            9
 609           63            9
 702           71            2
 703           71            3
 704           71            4
 704           72            4
 705           71            5
 706           71            6
 706           72            6
 706           73            6
 708           71            8
 708           72            8
 708           74            8
 709           71            9
 709           73            9
 802           81            2
 803           81            3
 804           81            4
 804           82            4
 805           81            5
 806           81            6
 806           82            6
 806           83            6
 807           81            7
 809           81            9
 809           83            9
 902           91            2
 903           91            3
 904           91            4
 904           92            4
 905           91            5
 906           91            6
 906           92            6
 906           93            6
 907           91            7
 908           91            8
 908           92            8
 908           94            8

with the smallest USA at 012 and the largest at 908.

 


  Posted by Charlie on 2013-01-21 21:03:37
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