We combine the observed distribution of Type Ia supernova (SN Ia) ^(56)Ni yields with the results of sub-Chandrasekhar detonation and direct collision calculations to estimate what mass white dwarfs (WDs) should be exploding for each scenario. For collisions, the average exploding WD mass must be peaked at ≈0.75M_☉, significantly higher than the average field WD mass
of ≈0.55–0.60M_☉. Thus, if collisions produce most SNe Ia, then a mechanism must exist that favours higher mass WDs. On the other hand, in old stellar populations, collisions would naturally result in low-luminosity SNe Ia, and we suggest these may be related to 1991bg-like events. For sub-Chandrasekhar detonations, the average exploding WD mass must be peaked at ≈1.1M_☉. This is similar to the average total mass in WD–WD binaries, but it is not
clear whether double degenerate mergers would synthesize sufficient ^(56)Ni to match observed yields. If not, then actual ≈1.1M_☉ WDs would be needed for sub-Chandrasekhar detonations. Since such high-mass WDs are produced relatively quickly in comparison to the age of SN Ia
environments, this would require either accretion on to lower mass WDs prior to ignition or a long time-scale between formation of the ≈1.1M_☉ WD and ignition
