What happens if neither Trump nor Clinton gets 270 electoral votes?

[Gaybutton]

I'm seeing some news reports saying it is now possible, considering third party candidates, that neither Trump nor Clinton will get the magic number - 270 electoral votes.

There is even a possibility of a tie - 269 electoral votes each.

If neither candidate reaches 270 electoral votes, what happens next?
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The 12th Amendment to the Constitution requires that candidates for President and Vice President receive a majority of electoral votes (currently 270 or more of a total of 538) to be elected. If no candidate receives a majority, the President is elected by the House of Representatives, and the Vice President is elected by the Senate. This process is referred to as contingent election.

In the House, the President is elected from among the three candidates who received the most electoral votes. Each state casts a single vote for President, which is arrived at by an internal vote conducted within each state delegation. A majority of 26 or more state votes is required to elect. The District of Columbia, however, does not participate in contingent election of either the President or Vice President.

In cases where a state has only one Representative, that Member decides the state vote. In the Senate, the Vice President is elected from among the two candidates for Vice President who received the most electoral votes, with each Senator casting a single vote. A majority of the whole Senate, 51 or more votes, is necessary to elect.

Contingent election would be conducted by the newly elected Congress immediately following the joint session (held on January 6 of the year following a presidential election) that counts electoral votes.

If the House is unable to elect a President by January 20 (when the new presidential and vice presidential terms begin), the Vice President-elect serves as Acting President until the impasse is resolved. If the Senate is unable to elect a Vice President by January 20, then the Speaker of the House serves as Acting President.

Full article: http://electoralcollegehistory.com/elec ... ngress.asp

What the article does not say is if no candidate has been elected by January 20, then once Congress does resolve the election, how long after that does the inauguration of the new president take place.

I'm also confused as to which Congress would hold the election if no decision is reached by the time the new Congress is seated. Would the election then be decided by the new Congress?

Also, as far as I can tell, there is no way to know how long a contingent election could drag on. Maybe it could be months, even years. For all I know, by the time Congress has elected either Trump or Clinton, it could already be time for the 2020 election.

Once again, I wouldn't want to be a history teacher 50 or 100 years from now trying to explain this election to students. I can't even explain it now . . .