What's in the latest Washington Post-ABC News tracking poll (Video: Peter Stevenson/The Washington Post)

Two things that may seem contradictory at first are true of this election campaign in its final days:

1. Donald Trump is making up ground on Hillary Clinton.

2. Hillary Clinton still has a solid hold on the 270 electoral votes she needs to be elected president in six days’ time.

But how solid is the Democratic nominee's grip on that 270? I thought it would be worth fiddling around with our terrific electoral map tool to see how many realistic paths Trump has to 270 electoral votes as a way of answering that question. (By realistic, I mean could actually happen. So, no, Trump winning California is not an option I explored.)

1. Trump 272, Clinton 266

This map gives the Republican nominee all of the states Mitt Romney won in 2012, as well as Colorado, Florida, Iowa, Ohio and New Hampshire. Of that group, Iowa and Ohio look like the easiest lifts for Trump, while Colorado and New Hampshire look the toughest.

2. Trump 273, Clinton 265

I’m skeptical that Trump will get over the hump in North Carolina, where the bathroom bill signed into law by Gov. Pat McCrory (R) has damaged the Republican brand. But, even if you give North Carolina to Clinton, the map above gets Trump to the White House. He would need to add Colorado, Florida, Iowa, Nevada, New Hampshire, Ohio and Wisconsin to do it, though. Possible? Yes. But not easy, given where he is on the map today.

3. Trump 269, Clinton 269 (option 1)

Yes, this could actually happen. The map above gives Trump wins in five states President Obama carried in 2012: Florida, Iowa, Nevada, New Hampshire and Ohio. It also assumes that Maine and Nebraska — both of which award their electoral votes by congressional district — cancel one another out. (Trump could win Maine’s 2nd District; Clinton could win Nebraska’s 2nd District.)

If this map actually came to pass, the election would go to Congress, where each state would get a single vote — a scenario that would almost certainly elect Trump.

4. Trump 269, Clinton 269 (option 2)

Similar to the map above in #3, but this one gives Trump Wisconsin — a state where Republicans are increasingly optimistic they have a chance at winning.

The big take-aways from the four maps above are that reasonable paths do exist for Trump to win, and his ceiling in terms of electoral votes is extremely low.

None of the four maps gives Trump more than 273 electoral votes — barely more than the minimum of 270 he would need. Even in the rosiest scenarios I cooked up using our electoral map tool, I could barely get Trump to 300 electoral votes. A part of that low ceiling is due to the sort of campaign he has run and the image he has cultivated. But a far larger part is the demographic problems that plague the Republican Party writ large. Those problems are likely to be blamed on Trump if he loses but actually aren’t all — or even mostly — his fault.

What Donald Trump is doing on the campaign trail

MANCHESTER, NH - NOVEMBER 7: Republican presidential candidate Donald Trump speaks during a campaign event at SNHU Arena in Manchester, NH on Monday November 07, 2016. (Jabin Botsford/The Washington Post)