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HeaRT OF VENUS (Posted on 2011-09-18) Difficulty: 3 of 5
Solve the following alphametic, given that two are primes and one is a composite:

SEVEN - THREE = FOUR

BONUS: Without the restriction of the number of composites and primes in the alphametic, how many different solutions are there?

  Submitted by Dej Mar    
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Solution: (Hide)
U V E F O T S R H N
0 1 2 3 4 5 6 7 8 9

SEVEN - THREE = FOUR
62129 - 58722 = 3407

62129 and 3407 are the two primes with 58722 as the composite. Without the restriction of the number of primes and composites there would be 38 possible solutions for the alphametic. Including the solution, those numbers are:

SEVEN THREE FOUR
23439 15633 7806
23439 17633 5806
23938 16533 7405
23938 17533 6405
24349 16544 7805
24349 17544 6805
25758 16355 9403
25758 19355 6403
31519 24811 6708
31519 26811 4708
35159 26455 8704
35159 28455 6704
36061 27566 8495
36061 28566 7495
41517 32611 8906
41517 38611 2906
41918 35711 6207
41918 36711 5207
45157 36255 8902
45157 38255 6902
52728 43622 9106
52728 49622 3106
56368 47266 9102
56368 49266 7102
61219 53811 7408
61219 57811 3408
62129 53722 8407
62129 58722 3407
71315 62411 8904
71315 68411 2904
71814 62311 9503
71814 69311 2503
73135 64233 8902
73135 68233 4902
82526 73422 9104
82526 79422 3104
84346 75244 9102
84346 79244 5102

It might be interesting to note that two of the solutions (where SEVEN=36061) U=9, with the other 36 solutions U=0.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutioncomputer solutionCharlie2011-09-18 17:01:49
Some ThoughtsPARTIAL SOLUTIONAdy TZIDON2011-09-18 14:43:06
Some ThoughtsPARTIAL SOLUTIONAdy TZIDON2011-09-18 14:43:03
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