Dan wrote:

> When I solved that puzzle I was thinking more in terms of cardinality of sets (if two sets have the same cardinality there is a bijection between them), but I was not concerned with choosing a particular bijection.

Okay, it's good that we're clearing this up, then. This is one of many situations where having a specific bijection is much better than merely knowing one exists, which can be determined just by counting. For example, there's a big difference between knowing you have one wife and knowing who she is.