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

Home > Numbers
Nevo and Oven (Posted on 2012-07-04) Difficulty: 3 of 5
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.

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

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution 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  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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information