I posted Puzzle #11 on Pi Day (3/14/15 in the U.S.). I noted that the sequence of numbers in 3.14159… reflects not just **π**, but also **ten**, the base we use for our numbers.

The question was:

**What is 30.12120111…?**

After no answers showed up on this blog for two months, I posted the puzzle to the Brainteaser Forum at Wilmott.com. “Traden4Alpha”, a brilliant Wilmott member, made quick work of the problem and posted this answer:

It’s a useful constant for those with pi fingers who are visiting Earth.

What does this mean? If somehow these aliens each had **π **fingers, then they might have developed a number system based on **π**. When visiting Earth, the aliens must account for humanity’s choice of **ten** as our number base. It would help them to know that **30.12120111… **is **ten** in base **π**.

To see how this works, recall that our number system is built on powers of ten:

**π**=**3×**10^{0} + **1×**10^{-1} + **4×**10^{-2} + **1×**10^{-3} +** 5×**10^{-4} + **9×**10^{-5} + …

This equation is an infinite assembly manual* for making **π** from powers of **ten**. We start with three ones, then one tenth, then four hundredths, and so on.

Similarly, the aliens could write **ten** in base **π** like this:

**ten**=**3×**π^{1} + **0×**π^{0} + **1×**π^{-1} + **2×**π^{-2} + **1×**π^{-3} +** 2×**π^{-4} + **0×**π^{-5} + …

I appreciate that Traden4Alpha found such a practical application for this little puzzle.

*At least it’s not one of these Ikea manuals.