There were a lot of delegates at stake on Tuesday night -- more than on any single day since March 15, when Ohio and Florida went to the polls. That meant that presidential candidates had a good opportunity to shift their totals in one direction or the other. For Donald Trump, it was a chance to close in on the 1,237 delegates he needs in order to win the nomination. For Bernie Sanders, a chance to close in on Hillary Clinton's lead.

Only Trump was successful.

With his wins Tuesday night, Trump has now passed the 50 percent mark on pledged delegates won. (The numbers below are a Post analysis of delegate estimates from delegate-watcher Daniel Nichanian.) That's despite not having won more than half of the votes -- a quiet reminder that the Republican system is indeed rigged, on behalf of the front-runner.

Trump's surprisingly big wins meant that he closed in on 1,237 more than would have been expected, and dropped his magic number -- the percentage he still needs to win -- to about 56 percent. After New York, the magic number was 63 percent, but since he won more than 90 percent of the pledged delegates on Tuesday, the percentage dropped.


And that's only including pledged delegates. For really the first time, Trump won the commitments of most of the unpledged delegates in a state -- at least 30 in Pennsylvania -- meaning that his path to 1,237 is actually a bit easier than the 56 percent magic number. Since we're only including pledged delegates (those Pennsylvania delegates aren't required to vote for him), the number is slightly higher.

But certainly attainable. Again, he's won a majority of delegates with a plurality of votes. He only needs a slight majority of what remains, and will only need a plurality to do so, assuming that Ted Cruz and John Kasich stick around until California votes on June 7. As Nate Cohn points out at The Upshot, good performances in Indiana and California (the last two big states on the GOP calendar) would likely allow Trump to clinch the nomination.

Since so many delegates were taken off the table Tuesday, it allowed Trump's numbers to move a lot. The same thing happened to Bernie Sanders, but in the other direction.

With some delegates still outstanding, Sanders would need to win every single remaining delegate to clinch the nomination. (This is excluding superdelegates, the unbound delegates on the Democratic side.) He'd need to win about 65 percent of what's left in order to pass Clinton (and be able to make the case that he should get the nomination). In the Democrats' proportional system of distribution, that's simply not going to happen.


The movement in the lines on those two graphs are a reminder of why Tuesday night was so important. Trump's magic number dropped a lot -- more than expected. Sanders's spiked -- prompting him to all but concede defeat.

Math is the bane of the existence of a lot of elementary school students. Sometimes it's frustrating for adults, too.