(In reply to Low 300s ??
by ed bottemiller)
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 i1-i3=i4-i2
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 (non-randomly 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 2010-07-17 09:05:23