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 \(7¢, because $~$2^6 < 101 < 2^7$~$\) or 3 wheels \(one per digit, because a wheel stores a digit, for a total of 9¢\), in which case the coins are better\. But wheels are better for storing the number 8000 \(13 coins v 4 wheels, as you can verify\)\. And coins are better for storing the number 15,000 \(14 coins v 5 wheels\)\. At 3¢ per wheel, which you buy depends on which number you want to store\.
I think this paragraph and the preceding paragraph would be great opportunities for hidden-text homework problems.