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Raise Aries (Posted on 2010-04-16) Difficulty: 2 of 5
Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of alphametic relationships. Each of A and R is nonzero.

(i) Each of RAISE and ARIES is a perfect square, and:

(ii) I + S and A + E are consecutive primes.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

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Solution computer solution | Comment 2 of 3 |
  5   dim Used(9)
 10   for R=1 to 9
 20     Used(R)=1
 30   for A=1 to 9
 40    if Used(A)=0 then
 50     :Used(A)=1
 60   :for I=0 to 9
 70   :if Used(I)=0 then
 80     :Used(I)=1
 90   :for E=0 to 9
100   :if Used(E)=0 then
110     :Used(E)=1
120   :for S=0 to 9
130   :if Used(S)=0 then
140     :Used(S)=1
200     :Raise=R*10000+A*1000+I*100+S*10+E
210     :Aries=A*10000+R*1000+I*100+E*10+S
220     :Sr=int(sqrt(Raise)+0.5)
230     :if Sr*Sr=Raise then
240     :Sr=int(sqrt(Aries)+0.5)
250     :if Sr*Sr=Aries then
260       :P1=I+S:P2=A+E
270       :if nxtprm(P1-1)=P1 and nxtprm(P1)=P2 then
280         :print Raise;Aries,int(sqrt(Raise)+0.5);int(sqrt(Aries)+0.5),P1;P2
290       :endif
300     :endif
320     :endif
450     :Used(S)=0
460    :endif
470   :next
480     :Used(E)=0
490    :endif
500   :next
510     :Used(I)=0
520    :endif
530   :next
540     :Used(A)=0
550    :endif
560   next
570     Used(R)=0
580   next
finds
                 square roots
                 ------------
 raise  aries    raise  aries      i+s  a+e
 18769  81796     137    286        13  17

  Posted by Charlie on 2010-04-16 16:35:41
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