Happy Numbers

At the start of the year, people often ask simple questions. Is this year going to be lucky? Will it turn out well?

The Same Rule, Different Fates

At the start of the year, people often ask simple questions. Is this year going to be lucky? Will it turn out well? That’s how I stumbled (again) on a small numerical curiosity called happy numbers.

The rules are almost trivial.

1. Take a number.
2. Split it into digits.
3. Square them.
4. Add them up.
5. Repeat

That’s it. No clever tricks. No advanced maths. Just iteration. And yet - something interesting happens. Some numbers quietly settle down. They converge to 1 and stop changing. These numbers are called happy.

Others never do.

They fall into a loop and keep cycling forever.

Same rule, different fates.