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, OVEN – V*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.
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 3527
NONE 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 |
computer solution
