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EVEN remains even (Posted on 2011-02-20) Difficulty: 4 of 5
ODD+ODD=EVEN is an alphametic puzzle in base b ( b=<16.) What 4 digit numbers represent an integer EVEN, evaluated in all the bases in which valid solutions exist.

  Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)
Solution: (Hide)
1310 as EVEN is a valid answer for any even base 2*b ,b>2
Let O;D;D be represented by b+1;b;b
Then EVEN
"units" = b+b= 2b = 0 and carry=1 N
"tens"= 1 (carried from b+b=2b and carry=1) E
"hundreds" =3 ( b+1+b+1+1=3 and carry=1) V
"thousands"=1 E
16 was set by me as a limit, to facilitate use of alphametic solver.

see Charlie's list OF all possible solutions.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/Tipsre: computer solution + analytical spoilerAdy TZIDON2011-02-20 17:51:34
Solutioncomputer solutionCharlie2011-02-20 16:33:02
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