shoelaces and aglets

[Brendan McKay]

* N. J. A. Sloane <njas at research.att.com> [050516 23:08]:
> PS  I changed it again to read:
> 
> %N A106744 Given n shoelaces, each with two aglets; sequence gives number of ag\
> let pairs that must be picked up to guarantee that the probability that no shoe\
> lace is left behind is > 1/2.

I don't see the point of selecting pairs rather than single aglets.
Since the choosing is done without replacement, the number of pairs
required is just the number of singletons required rounded up to a
multiple of 2 and then divided by 2. So counting singletons gives
more information. Or did I miss something?

Brendan.