[jwpeddle]

Not sure what you're refering to by "count" here. There's nothing to count. What matters is everybody coming into the knowledge that everybody knows at least one person has blue eyes. This takes a prompt about that, which is the foreigner's speech. If the foreigner doesn't cause them to start sorting themselves into blue eyes/not blue eyes groups, there's no basis for them to start deducing anything.

[axus]

Counting is how they measure the days passed versus how many blue-eyed people they see. I'm sure you're right, but I have to check the assumption that seeing everyone is the same as hearing a fact about everyone.