## Ken's Puzzle of the WeekSum Pyramid

```    8
3   5
2   1   4
```

Place unique positive integers into a pyramid such that each number equals the sum of the two numbers below it.  Minimize the top number.  A solution for three rows is above.  Solve for 4, 5, and 6 rows.  (or more...).  To remove reflections in submissions, let the lower left corner be less than the lower right.

Source: Original.  Based on what ought to be a classic puzzle I found in the recent Games Magazine, with 6 rows and the top number of 100.

Solutions were received from Keith F. Lynch, Joseph DeVincentis, Philippe Fondanaiche, Alan O'Donnell, Luis Baztan, Kirk Bresniker, David Madfes, Claudio Baiocchi.  Joe sent a simple summary for 4, 5 and 6 rows:

98
46  52
26  20  32
17   9  11  21
12   5   4   7  14
10   2   3   1   6   8

43
20  23
12   8  15
9   3   5  10
7   2   1   4   6

The two solutions for a 4-pyramid of 20 can be seen embedded in the above solutions.

Most solvers pointed me to several other sites where this has been analyzed:
http://www.research.att.com/~njas/sequences/A028307
http://www.research.att.com/~njas/sequences/a028307.txt
http://www.lacim.uqam.ca/~plouffe/OEIS/txt/a028307.txt
Mail to Ken