"Is this a typo? Shouldn't you buy coins if they..."


by Eli Tyre Sep 17 2017

So digit wheels are worth more than 3x as much as a coin, and less than 4x\. How can we find the right price exactly? We could use exactly the same argument as above to check whether 3\.5¢ is too high or too low, except that it's not clear what it would mean to buy "three and a half coins\." We can get around that problem by considering ten\-packs of coins vs ten\-packs of digit wheels\. If wheels cost 3\.5¢ and coins cost 1¢, then with 35¢, you could either buy 10 wheels or 35 coins\. Which encodes more possibilities? The coins, because $~$10^{10} < 2^{35}.$~$ Thus, by a generalized version of the argument above, for numbers sufficiently large, the coins are a better deal than the wheels — at that price, you should buy wheels\.

Is this a typo? Shouldn't you buy coins if they are a better deal? Or am I missing something?