No problem about this in the 'New' Liturgy. Lent begins on Ash Wednesday. But for obscurantist fuddy-duddies who stick with the Old Rite (and for Ambrosians), matters are far less simple.
The First Sunday in Lent is called in capite Quadragesimae. Lenten Office Hymns don't begin until First Vespers of Sunday. You stick with Pars hiemalis Breviarii Romani until then. And, as Gueranger puts it, "Although the law of Fasting began [on Ash Wednesday], yet, Lent [Careme], properly so called, does not begin till the Vespers of Saturday next. In order to distinguish the rest of Lent from these four days which have been added to it, the Church continues to chant Vespers at the usual hour, and allows her Ministers to break their fast before having said that office. But, beginning with Saturday, the Vespers will be anticipated; every day (Sundays excepted) they will be said at such an early hour that when the Faithful take their full meal, the Evening Office will be over. It is a remnant of the discipline of the primitive Church, which forbade the Faithful to break their fast before sun-set, in other words, before Vespers or Even-song".
The mathematics and history of Lent were sorted out by Canon Callewaert, of Bruges, and Dr G G 'Patrimony' Willis, Vicar of Wing. In case anybody is interested, I give a summary of the facts.
(1) Originally, the only Fast around seems to have been the very primitive Paschal Fast, on Good Friday and Holy Saturday. Lent hadn't been invented.
(2) For reasons connected with the instruction of the catechumens and the discipline of penitents, a forty-day preparation for this was added to the already existing Paschal Fast. Forty days back from Maundy Thursday gets you back precisely to the First Sunday in Lent.
(3) A later age forgot the distinction between Lent and the Paschal Fast and considered them both just "Lent". It also wished to take account of the fact that, in the Roman Rite, one does not fast on Sundays. To get forty days of fast in before Easter Day, you need 6 X a week of 6 fasting days: = 36 days; + four extra days: = 40; which gets you back to .... Ash Wednesday.
(4) But the Liturgy ... at least, the Divine Office ... endearingly ... never caught up with these latest mathematics ... until the Age of Archbishop Bugnini the Great Elephant Fetichist.
Hence the anomalous status of the four days this week "After the Ashes". A whimsy, surely, in that it took a twentieth century which had pretty well given up even the memory of fasting, to add these four days to the full Lenten status.
Sometimes I wonder why ecumenical enthusiasts never lecture us on the need to follow the Byzantines and to have a real fasting Lent.
I will be fair: I can see the point of Hannibal Bugnini's abolition of the Gesimas and his elimination of the status-anomaly of the days post cineres. Taste-wise, I suppose it's ultimately a question of whether you like your Calendar neat and clean-cut with no little puzzles side-issues to worry you or to intrigue you; or whether you prefer it weirdish and interesting.
Incidentally, S Gregory the Great, taking Lent as beginning on Sunday and ending on the early morning of Easter Sunday, calculated that it consisted of 6X7=42 days; from which you subtract the unfasting Sundays (42-6=36) and then add half a day for the fasting part of Easter Sunday (=36.5 days): which is a tithe of the year!
Sometimes I feel immensely grateful that the Fathers lacked computers. Otherwise, they would undoubtedly have spent their entire time devising ever more arcane mathematics on their flickering screens, and would never written any Theology.