Let Me Tell You A Story
Here, the residents have a custom of congregating at a predetermined place and time to shake hands and do so only on one day of the Handshake-ian calender.
The peculiar thing about this custom is that they can do only an odd number of handshakes with all the other residents present on the auspicious day, lest they incur the wrath of the Handshake lords.
Let the number of people who take part in this custom each year be N.
The question is, what is \( N\) mod \(2\) ?