Let's look at what we do know - and rate the various options.
1. Nobody wants another early general election: That view is shared by all shades of opinion at Leinster House. An opinion poll published yesterday suggested that only about one in seven voters wants to see an early return to the polls.
But those wishes will not of themselves stave off another election. In 1981/1982, with the economy teetering on the brink of bankruptcy, it took three elections over 18 months to give stable government.
Avoiding a general election requires key people in several parties to change their stances. Somebody or something has to give here. We have seen it happen before in our recent history. In 1989, Charlie Haughey breached a core Fianna Fáil value and shared cabinet seats with the breakaway Progressive Democrats.
In 1992, Dick Spring of Labour got over his antipathy for the politics of Albert Reynolds's Fianna Fáil and joined a coalition. In 1994, John Bruton put aside his mistrust of the Democratic Left to form a rainbow coalition. This time the gaps to be bridged look wider and the obstacles to be overcome appear bigger. But a formula can be found.
2. A Sinn Féin coalition with all other parties - bar Fianna Fáil and Fine Gael: This was talked-up by Mary Lou McDonald and her leadership colleagues in the course of the election campaign.
But last Friday morning, Sinn Féin's housing spokesman Eoin Ó Broin said that such a left-leaning coalition led by his party, and made up of left-wing parties and individuals, was just not possible. After just two days of effort, he said there would not be sufficient numbers in the new Dáil.
He was criticised by People Before Profit's Dún Laoghaire TD Richard Boyd-Barrett, who said Sinn Féin had "thrown in the towel" too early. But Solidarity's Cork North-Central TD Mick Barry said the Dáil numbers were not there and urged measures to ensure it may be there next time out.
Fianna Fáil and Fine Gael TDs, including Taoiseach Leo Varadkar, also criticised Sinn Féin for being half-hearted about its pan-left coalition efforts. Sinn Féin countered by accusing "the two big parties" of disregarding its 24pc support and also warned groups like the Green Party and Social Democrats not to help either Fianna Fáil or Fine Gael get into government.
Given all that hot air, it appears safe to file this one as "less likely". Not impossible - rather improbable.
3. Fianna Fáil-Sinn Féin-Green Party and possibly others: Fianna Fáil has ruled this out after its TDs and senators met for over four hours last Thursday. During a long campaign, its leader Micheál Martin not only shut down and locked out that option, he actually nailed the door shut on it many times.
That does not mean it will definitely not come around again, especially if this process drags on without success.
The move has led to Sinn Féin again playing the "face-at-the-window", arguing the party, and its voters, are being excluded by the "old boys' club".
It's a useful propaganda tool - but it does not stand scrutiny. Yes, Sinn Féin did have a great election with the biggest vote share. But another way of looking at things is that three out of four people did not vote for Sinn Féin and one citizen's vote carries no more weight than that of another.
Mr Martin does want to provide a government and wants to be Taoiseach. But, like most parties, whichever coalition option emerges must be endorsed by the membership at a special conference.
This one is again less likely to happen.
4. Fianna Fáil-Fine Gael-Green Party and possibly others: The grandson of Fianna Fáil's founder, Éamon Ó Cuív, let the cat out of the bag on this one last week when he went on Raidío na Gaeltachta after his parliamentary colleagues ruled out Sinn Féin.
'Dev Óg', as he's known to some, said Micheál Martin wanted Fianna Fáil to lead government and this eventually was the only permutation which added up.
Mr Ó Cuív said his party's grassroots were strongly opposed as were some of his colleagues.
The reality is all three parties would have a hard sell to their members on this one. But it should go nicely over the magic 80 TDs needed to give a majority.
Fine Gael TDs and senators may also be strongly opposed. Having gone from 75 TDs in 2011, to 50 in 2016, and down to 35 this time, some see opposition and a rebuild as the only way to avoid extinction. There could be a very noisy first meeting of the Fine Gael parliamentary party today.
This one has lots and lots of snags - not least the prospect of leaving the opposition field wide open to Sinn Féin. But the arithmetic is compelling.
5. A Fianna Fáil-led conglomerate of the Green Party, Social Democrats, others and a large group of Independents: Achieving numbers here would be hard work.
Some amenable rural Independents might struggle to overcome their anti-Green political rhetoric. In fact, some of them are talking about re-grouping as a counterweight and alternative to the Green Party in coalition.
This one might have to involve also coaxing Labour, which has already said it is heading into opposition no matter what. At first glance, this one appears to have a problem for every solution.
But it could emerge - eventually - as the 'dark horse' option.