  We consider the following conjecture proposed by Cornu\'ejols, Guenin and
Margot: every ideal minimally non-packing clutter has a transversal of size 2.
For a clutter C, the tilde clutter is the set of hyperedges of C which
intersect any minimum transversal in exactly one element. We divide the
(non-)existence problem of an ideal minimally non-packing clutter D into two
steps. In the first step, we give necessary conditions for C = the tilde
clutter of D when a clutter D is an ideal minimally non-packing clutter. In the
second step, for a clutter C satisfying the conditions in the first step, we
consider whether C has an ideal minimally non-packing clutter D with C= the
tilde clutter of D. We show that the clutter of a combinatorial affine plane
satisfies the conditions in the first step. Moreover, we show that the clutter
of a combinatorial affine plane does not have any ideal minimally non-packing
clutter of blocking number at least 3.
