The ImpressionRank of a web page (or, more generally, of a web site) is the number of times users viewed the page while browsing search results. ImpressionRank captures the visibility of pages and sites in search engines and is thus an important measure, which is of interest to web site owners, competitors, market analysts, and end users. All previous approaches to estimating the ImpressionRank of a page rely on privileged access to private data sources, like the search engine's query log. In this paper we present the first external algorithm for estimating the ImpressionRank of a web page. This algorithm relies on access to three public data sources: the search engine, the query suggestion service of the search engine, and the web. In addition, the algorithm is local and uses modest resources. It can therefore be used by almost any party to estimate the ImpressionRank of any page on any search engine. En route to estimating the ImpressionRank of a page, our algorithm solves a no...