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 looking at the 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.

Donald Trump's most controversial quotes Show all 14 1 /14 Donald Trump's most controversial quotes Donald Trump's most controversial quotes On Isis: "Some of the candidates, they went in and didn’t know the air conditioner didn’t work and sweated like dogs, and they didn’t know the room was too big because they didn’t have anybody there. How are they going to beat ISIS?" Getty Donald Trump's most controversial quotes On immigration: "I will build a great wall — and nobody builds walls better than me, believe me —and I’ll build them very inexpensively. I will build a great, great wall on our southern border, and I will make Mexico pay for that wall. Mark my words." Reuters Donald Trump's most controversial quotes On Free Trade: "Free trade is terrible. Free trade can be wonderful if you have smart people. But we have stupid people." PAUL J. RICHARDS | AFP | Getty Images Donald Trump's most controversial quotes On Mexicans: "When Mexico sends its people, they’re not sending their best. They’re sending people that have lots of problems. They’re bringing drugs. They’re bringing crime. They’re rapists." Getty Donald Trump's most controversial quotes On China: "I just sold an apartment for $15 million to somebody from China. Am I supposed to dislike them?... I love China. The biggest bank in the world is from China. You know where their United States headquarters is located? In this building, in Trump Tower." Getty Images Donald Trump's most controversial quotes On work: "If you're interested in 'balancing' work and pleasure, stop trying to balance them. Instead make your work more pleasurable." AP Donald Trump's most controversial quotes On success: "What separates the winners from the losers is how a person reacts to each new twist of fate." Donald Trump's most controversial quotes On life: "Everything in life is luck." AFP Donald Trump's most controversial quotes On ambition: "You have to think anyway, so why not think big?" Getty Images Donald Trump's most controversial quotes On his opponents: "Bush is totally in favour of Common Core. I don't see how he can possibly get the nomination. He's weak on immigration. He's in favour of Common Core. How the hell can you vote for this guy? You just can't do it." Reuters Donald Trump's most controversial quotes On Obamacare: "You have to be hit by a tractor, literally, a tractor, to use it, because the deductibles are so high. It's virtually useless. And remember the $5 billion web site?... I have so many web sites, I have them all over the place. I hire people, they do a web site. It costs me $3." Getty Images Donald Trump's most controversial quotes On Barack Obama: "Obama is going to be out playing golf. He might be on one of my courses. I would invite him. I have the best courses in the world. I have one right next to the White House." PA Donald Trump's most controversial quotes On himself: "Love him or hate him, Trump is a man who is certain about what he wants and sets out to get it, no holds barred. Women find his power almost as much of a turn-on as his money." Getty Images Donald Trump's most controversial quotes On America: "The American Dream is dead. But if I get elected president I will bring it back bigger and better and stronger than ever before and we will make America great again." GETTY

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.