All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 HeaRT OF VENUS (Posted on 2011-09-18)
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?

 See The Solution Submitted by Dej Mar No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution Comment 3 of 3 |

10     dim Used(9)
20     for S=1 to 9
30      if Used(S)=0 then
40        :Used(S)=1
50     :for T=1 to 9
60     :if Used(T)=0 then
70        :Used(T)=1
80     :for F=1 to 9
90     :if Used(F)=0 then
100        :Used(F)=1
110     :for E=0 to 9
120     :if Used(E)=0 then
130        :Used(E)=1
140     :for V=0 to 9
150     :if Used(V)=0 then
160        :Used(V)=1
170     :for N=0 to 9
180     :if Used(N)=0 then
190        :Used(N)=1
200        :Seven=10000*S+1010*E+100*V+N
210     :for H=0 to 9
220     :if Used(H)=0 then
230        :Used(H)=1
240     :for R=0 to 9
250     :if Used(R)=0 then
260        :Used(R)=1
270        :Three=10000*T+1000*H+100*R+11*E
280     :for O=0 to 9
290     :if Used(O)=0 then
300        :Used(O)=1
310     :for U=0 to 9
320     :if Used(U)=0 then
330        :Used(U)=1
340        :Four=1000*F+100*O+10*U+R
350        :if Seven-Three=Four then
355         :inc Sct
360         :print Seven;Three;Four,
370         :PCt=0
380         :if prmdiv(Seven)=Seven then inc PCt:Plst="7":else Plst="":endif
390         :if prmdiv(Three)=Three then inc PCt:Plst=Plst+"3":endif
400         :if prmdiv(Four)=Four then inc PCt:Plst=Plst+"4":endif
403         :print PCt,Plst
410        :endif
420        :Used(U)=0
430      :endif
440     :next
450        :Used(O)=0
460      :endif
470     :next
480        :Used(R)=0
490      :endif
500     :next
510        :Used(H)=0
520      :endif
530     :next
540        :Used(N)=0
550      :endif
560     :next
570        :Used(V)=0
580      :endif
590     :next
600        :Used(E)=0
610      :endif
620     :next
630        :Used(F)=0
640      :endif
650     :next
660        :Used(T)=0
670      :endif
680     :next
690        :Used(S)=0
700      :endif
710     next
720     print Sct

finds

23439  17633  5806      0
23938  17533  6405      0
24349  17544  6805      0
25758  19355  6403      0
23439  15633  7806      0
23938  16533  7405      0
24349  16544  7805      0
25758  16355  9403      1      4
31519  26811  4708      0
31519  24811  6708      0
35159  28455  6704      1      7
36061  28566  7495      1      7
35159  26455  8704      1      7
36061  27566  8495      1      7
41517  38611  2906      1      3
41918  36711  5207      0
41918  35711  6207      0
45157  38255  6902      0
41517  32611  8906      1      3
45157  36255  8902      0
52728  49622  3106      0
56368  49266  7102      0
52728  43622  9106      0
56368  47266  9102      0
61219  57811  3408      0
62129  58722  3407      2      74
61219  53811  7408      0
62129  53722  8407      1      7
71315  68411  2904      0
71814  69311  2503      1      4
73135  68233  4902      0
71315  62411  8904      0
73135  64233  8902      0
71814  62311  9503      1      3
82526  79422  3104      0
84346  79244  5102      0
82526  73422  9104      0
84346  75244  9102      0
38

Indicating and listing 38 solutions when ignoring composites vs primes.

The first number following each solution is the number of those numbers that are prime. In most cases none is prime; in a few cases one of the numbers is prime, but in only one case are two of the numbers prime: 62129 - 58722 = 3407.

The remaining digits on the lines with primes are shorthand for which of the three numbers is/are prime. In the case of the solution with two primes this is 74, indicating SEVEN and FOUR represent primes: 62129 and 3407.

 Posted by Charlie on 2011-09-18 17:01:49

 Search: Search body:
Forums (0)