Four is Magic

Pick any number. Count the letters in its name. Repeat. You always end up at four.

Try a Number

Where Numbers Go

Each bubble is a number. Arrows show where it goes when you count its letters. Thicker arrows mean more numbers take that path. Everything ends at 4.

The Transition Table

For each number in your range: spell it, count the letters, and see where it lands.

Why Does This Always Work?

Here's the secret: when you spell out any number, the number of letters is almost always less than the number you started with.

The key idea: Spell out any number bigger than 4 and count its letters. You always get a smaller number than what you started with. Since the numbers keep getting smaller, they can't bounce around forever — they have to land somewhere. And that somewhere is always 4.

Look at how fast numbers shrink:

So no matter how big you start, after just one or two steps you're down to a small number. And once you're in the small numbers (say, under 20), there are only a few possible paths — and they all lead to 4.

Why 4 and not some other number? "Four" has exactly 4 letters. It's the only number in English where the letter count matches the number. In math, this is called an absorbing state — a place you can reach but can never leave. Every chain gets pulled down to small numbers, and 4 is the only small number that maps to itself, so everything ends up there.

Try setting the range above to something big, like 1 to 1000. You'll see that even a thousand different starting numbers all funnel through the same handful of small numbers on the way down to 4.