(In reply to
Low 300s ?? by ed bottemiller)
Ed,
Some further thoughts:
1. Let S be the set of marks on a Golomb Ruler of length EN and order x, in which i1+i2=i3+i4
2. Then it follows arithmetically that i1i3=i4i2
3. But S would not then be a Golomb Ruler.
It seems to follow that for any order, x, (here, 20) the last mark on a Golomb Ruler of order (x+1) represents the smallest possible number for which there is at least one (nonrandomly selected) subset, S, having the required number of x elements, with no stipulated duplicate. Accordingly, since the last mark on a Golomb Ruler of order 21 is 333, 332 should be the largest number for which it is possible to be certain, without further verification, that each and every randomly selected S will surely contain the stipulated duplicate.
(I am sure that there are much more elegant ways of expressing this!)
Edited on July 17, 2010, 10:39 am

Posted by broll
on 20100717 09:05:23 