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 Nevo and Oven (Posted on 2012-07-04)
Substitute each of the letters with a different base ten digit from 0 to 9. Each of the asterisks denote a digit, whether same or different. None of the numbers can contain a leading zero.

NEVO + NONE = OV*V and, OVENV*OO = E*O* where, each of NEVO and OVEN is a prime number.

Note: For an extra challenge, solve this puzzle without using a computer program.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

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 computer solution Comment 1 of 1

5   dim Used(9)
10     for N=1 to 9
20       Used(N)=1
30     for E=1 to 9
40      if Used(E)=0 then
50      :Used(E)=1
60    :for V=1 to 9
70     :if Used(V)=0 then
80      :Used(V)=1
90    :for O=1 to 9
100     :if Used(O)=0 then
110      :Used(O)=1
120   :
130      :Nevo=1000*N+100*E+10*V+O
140      :None=1000*N+100*O+10*N+E
145      :Oven=1000*O+100*V+10*E+N
150      :if prmdiv(Nevo)=Nevo and prmdiv(Oven)=Oven then
160         :Ovxv=Nevo+None
170         :if Ovxv\100=10*O+V and Ovxv@10=V then
580           :print Nevo,Oven
790         :endif
800       :endif
810   :
820      :Used(O)=0
830     :endif
840    :next
850      :Used(V)=0
860     :endif
870    :next
880      :Used(E)=0
890     :endif
900     next
910       Used(N)=0
920     next

finds only

3527    7253

for NEVO and OVEN respectively.

`NEVO  3527NONE  3735      ----OV*V  7262`

The above must be the solution as it's the only one that fits the firest equation. But, to check the second equation:

` OVEN    7253   7253-V*OO   -2077  -2177-----    ----   ---- E*O*    5176   5076 `

are the two substitutions for *'s that work.

It's interesting that the two primes involved both have each of the four single-digit primes as their digits, as did one of the solutions in Ady Tzidon's Complementary, my dear Watson. For the record, those permutations that are prime are listed on the right below, and those that aren't are listed on the left. Of course those ending in 2 or 5 don't work, but not all those ending in 3 or 7 work either.

`         2357 2375 2537 2573 2735         2753         3257 3275         3527 3572 3725 3752         5237         5273 5327 5372 5723 5732 7235         7253 7325 7352         7523 7532`

 Posted by Charlie on 2012-07-04 18:40:41

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