in reply to Simple Math Puzzle...

D(1,3,4,5) !=0 and D(1,2,4,5) != 9.
D5 cannot be 0 (it would be lowest),
D5 cannot be higher than 2 because d5(3) + d4(6) => d1(9) but d3 is hi
+ghest.
d5 must be 1|2, so d4 must be 2|4, so d1 must be > 3, so d3 must be > 
+4. D2 must be 0|1.

Eliminate the impossible

Digit   1 2 3 4 5
-----------------
0       x 0 x x x 
1       x 1 x x 1
2       x x x 2 2
3       x x x x x
4       4 x x 4 x
5       5 x 5 x x
6       6 x 6 x x
7       7 x 7 x x
8       8 x 8 x x
9       x x 9 x x 

Leaves us these choices.

        4 0 5 2 1
        5 1 6 4 2
        6   7
        7   8
        8   9

d1+1 = d3 means this further reduces to

40521 
50621 
60721
70821
80921 *
70842 
71842 
80942 *
81942 *

[download]

Eliminating those * that lack two prime digits leaves five+ six answers? (I think!)

(40521, 50621, 60721, 70821, 70842+, 71842)

+ Corrected. Thanks to crenz.

Examine what is said, not who speaks.
"Efficiency is intelligent laziness." -David Dunham
"When I'm working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." -Richard Buckminster Fuller

Replies are listed 'Best First'.
Re: Re: Simple Math Puzzle...(no code required?)
by crenz (Priest) on May 10, 2003 at 17:49 UTC

    I like the way how you showed to get the correct solutions; however, 70842 should be counted a solution as well -- it has two prime digits (2 and 7).

[reply]
Re^2: Simple Math Puzzle...(no code required?)
by hdb (Monsignor) on Jun 24, 2013 at 15:05 UTC

    The "two primes condition" follows from the fact that columns 4 and 5 have at most one prime, columns 2 has no prime, so there must be at least one prime in columns 1 and 3. But if digit 1 is 8, then digit 3 is 9, so no prime. This will directly create all solutions w/o any test, based on the implied order and your logic above: 

    use strict;
use warnings;
for my $two (0..1) {
  for my $five (($two+1)..2) {
    for my $one ((3*$five+1)..7) {
      print "$one$two".($one+1).(2*$five)."$five\n";
    }
  }
}

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