So what is the fair price for a digit wheel? 4¢ is still too high, because that makes a 10\-digit cost the same as a 16\-digit, and the 16\-digit is always better at that price\. What about 3¢? At that price, the answer is much less clear\. On the one hand, spending 3¢ on coins gets you the ability to write down only 8 possibilities, while spending 3¢ on wheels lets you write down 10 different possibilities\. On the other hand, if you're trying to store the number 101, you need either 7 coins \(7¢\) or 3 wheels \(9¢\), in which case the coins are better\. But wheels are better for storing the number 4097 \(13 coins v 4 wheels\)\. And coins are better for storing the number 10,001 \(14 coins v 5 wheels\)\. At 3¢ per wheel, which you buy depends on which number you want to store\.
Would be nice to be able to see explicitly why this is so. Not everyone can do powers of two in their heads.
Also, I just caught myself remembering that to compute how many wheels I need to store a number, I just need to count the digits! Would be nice to remind the reader of this on this page the first time it's needed.