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 Raise Aries (Posted on 2010-04-16)
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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 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 9100   :if Used(E)=0 then110     :Used(E)=1120   :for S=0 to 9130   :if Used(S)=0 then140     :Used(S)=1200     :Raise=R*10000+A*1000+I*100+S*10+E210     :Aries=A*10000+R*1000+I*100+E*10+S220     :Sr=int(sqrt(Raise)+0.5)230     :if Sr*Sr=Raise then240     :Sr=int(sqrt(Aries)+0.5)250     :if Sr*Sr=Aries then260       :P1=I+S:P2=A+E270       :if nxtprm(P1-1)=P1 and nxtprm(P1)=P2 then280         :print Raise;Aries,int(sqrt(Raise)+0.5);int(sqrt(Aries)+0.5),P1;P2290       :endif300     :endif320     :endif450     :Used(S)=0460    :endif470   :next480     :Used(E)=0490    :endif500   :next510     :Used(I)=0520    :endif530   :next540     :Used(A)=0550    :endif560   next570     Used(R)=0580   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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