In "A Pattern of Numbers" you were asked to find the relationship between numbers appearing in a pattern. This puzzle uses a similar, yet different, criterion.
Can you discover the relationship between the numbers and figure out what number belongs at the X in this pattern? The same rule applies to each set of numbers in the pattern.

  34  32  36  46  64  75  50  35  34
16  18  14  22   X  40  35  15  20  12

(In reply to re: No error in question Good, so far... by Mindrod)

Are you sure that there is a rule applied to determine the next number on the top row?  I don't read that as being part of the problem, it only asked that you determine the value of "X".

The only reason I ask is because this is listed as one of the "Truly Unsolved Puzzles", I'm assuming because of your last comment.  I don't see that there necessarily is a rule applied to get the next number on the top row. 

Had the last set (including the 12) not been there, it would be an interesting challenge to continue the chain where:

  cd
ab  de

a*b + c*d = de   AND  ab + de = cd

However, since the second part of that obviously doesn't hold, I don't see why the next number on the top row can't be chosen completely arbitrarily.  For example, I could make the next number on the top row 38, which would then make the next number on the bottom row 26 (1*2 + 3*8 = 26 and 12 + 26 = 38).  OR I could make it 36, which would make the next number on the bottom 20 (1*2 + 3*6 = 20; 12 + 20 does not equal 36, but that isn't a necessary condition of the pattern).

Is there something I'm missing?

Posted by tomarken on 2006-03-06 14:40:31