Can you come up with a plausible scenario where three US Presidential candidates split the electoral vote, then split the House vote such that no-one wins the House?
Almost happened back in 1824, with four candidates. Per the Constitution, the House got to choose among the top three: Adams, Jackson, and Crawford. The fourth candidate, Clay, threw his support to Adams, so Adams got a House majority.
Let's have a look on the recent third party runs in presidential elections:
1992: If Perot makes better, the Democrat-controlled House still elect Clinton.
1980: Anderson and Reagan split the Republican vote, but still the House is worried about re-electing Carter.
1968: Wallace convinces the Southern Democrats not to vote for Humphrey. Crazy shit happens.
1948: Same thing with Thurmond.
1924: Progressive from both parties rally to La Follette
1912: Same thing for Roosevelt.