The Hajj is Mathematically Impossible
You surely know already that the pilgrimage to Mecca is one of the five pillars of Islam: every adult who is physically and financially capable is expected to make the trip at least once. The idea that every Muslim on the planet must visit Mecca isn't a problem, but the idea that those visits must take place during one specific week of the year is.
Here's some random statistics gleaned from Google: in 2014, the Saudis allowed 2.1 million Muslims to make the Hajj. The world's Muslim population is 1.57 billion. The age of majority in Islam is 15 -- which, presumably, means a pilgrimage to Mecca doesn't "count" if you made the trip with your family before that age.
I don't know what percentage of Muslims are adults versus under-15s; the American census says that America's under-18 population is 23 percent. Of course, "Americans" have a much lower average birthrate, and thus a lower percentage of young people, than do "Muslims throughout the world."
What percentage of Muslims are under 15? Dunno, but I'll generously guess 40 percent -- which leaves 60 percent adults who are now obligated to do the Hajj if they can. That's roughly 942 million people. Of course, not all of them are physically or financially capable of making the pilgrimage, ever -- though more and more are able to every year, since a modern pilgrimage on an airplane is still considerably cheaper, quicker and easier than old-school treks across the seas and through the desert. How many of the world's 942 million Muslim adults cannot make the Hajj (and are exempted from the obligation) for health or financial reasons? I'll make a conservative estimate of 20 percent (though I suspect it's probably lower). That leaves 753.6 million adults expected to make the trip at least once.
Let's say an average death age of 70 (that's a worldwide average, including poor countries with much lower lifespans than ours) -- so, once Muslims turn 15 and reach adulthood, they have an average of 55 years, or rather 55 annual chances, to make the trip. But 753.6 million people divided by 2.1 million people whom the Saudis allow into Mecca for each Hajj means it'll take 359 years for every healthy and financially stable Muslim adult currently alive to get the chance to meet their obligation -- and even that's assuming every pilgrim is older than 15 and nobody ever makes the trip more than once.