That was how World Cup '94 turned out, when seven European nations made it to the last eight, only for the South American soccer giant to win the title for a record fourth time.
It could easily happen again.
On Sunday, France edged Paraguay 1-0 in the most dramatic of styles _ the first sudden-death overtime "golden goal" in World Cup history, and Denmark outplayed Olympic champion Nigeria 4-1 to reach the last eight.
With Italy already there along with Brazil, that makes it three out of four from Europe.
Today's games were an all-European encounter between the Netherlands and Yugoslavia, while Germany faced probably the weakest opening-round survivor, Mexico.
If the results went according to form, that would make it five European teams out of six, with Argentina the only other nation outside of Europe left in the competition.
Argentina faces England on Tuesday, the day Romania meets Croatia.
The entire nation was holding its breath while Paraguay held off the relentless forays by the host team. After his forwards laid siege to the Paraguayan defense, but were unable to break through it or get past inspired goalkeeper Jose Luis Chilavert, defender Laurent Blanc found a way through with six minutes of overtime left, avoiding a penalty-kick shootout.
Striker David Trezeguet headed down a cross from Robert Pires to Blanc, and the veteran defender drove the ball home from close range to create World Cup history.
"This is the most incredible joy to score in this way," Blanc said. "We have criticized the golden goal in the past, yet here we profited from it. What went through me when I scored was just indescribable."
Chilavert was left to console his teammates, many of them sprawled on the turf, crying.
"Our defense made life impossible for the French," Miguel Benitez said. "We tried until we almost left our lives on the field."
The sudden-death goal was introduced into the World Cup for the first time this year.
The Danes fired in two early goals against Nigeria, which showed a leaky defense all night.
Peter Moller and Brian Laudrup put the Danes ahead inside the first 12 minutes at the Stade de France, helped by poor defending and goalkeeping by the Nigerians.
"Obviously we needed to concentrate more at the beginning," Rufai said. "We lot it all in the first 15 minutes."
The Africans looked like a shadow of the team that triumphed in the Olympics two years ago, with star players such as Nwankwo Kanu, Finidi George and Jay-Jay Okocha misfiring.
Ebbe Sand and Thomas Helveg added the other goals in the second half before Tijani Babangida replied for the dispirited Nigerians.
While the Nigerians go home earlier than expected, the Danes will try and dethrone the Brazilians.
"We have to try," their Swedish coach, Bo Johansson, said. "Nigeria cannot try any longer. We will play against the best team in the world. We know we're not the best team in the world."
On this showing, neither is Nigeria.
"That's soccer, isn't it?" Finidi said. "It is really disappointing not to go through from the second round. But that's life."
The first of the extra 1,500 police were deployed Sunday as the English fans began arriving in Saint-Etienne for the match with Argentina. Local officials said bars would close at 11 p.m. today and Tuesday and police had orders to make arrests for public drunkenness.