New Democracy would have needed either the radical left-wring, Trotskyite party that finished second, or Pasok, the socialist party, that finished third, and one other partner. Possibly, the social democrat-type Party that finished sixth. These were the three pro-EU parties. But, obviously, these three parties couldn’t agree to terms.
The Trotskyite Party would have to assemble a coalition of ALL parties other than New Democracy and the neo-Nazi party. This is not as far-fetched as it sounds. But, I think this would require Pasok and the social democrat-type party to agree to leaving the Eurozone. Nobody will lend real money to the new Greek government. So, they will have to print the money to cover their precious government spending.
If no party can form a majority coalition, there will be another election. In a new round of voting, it is possible the 50 seat bonus that goes to the party that finishes first would go to the Trotskyite party. This would make it easier for it to assemble a ruling coalition. It would be Chile under Allende all over again.
IMHO the Greek Leftists caused the economic meltdown,with soicialistic false promises, and for that they should have no say in future govts over there.