Cluesday or National Cluesday (most commonly referred to as Cluesday) always occurs on the first Tuesday of every month. It is a day where the thousands of fans of the clue unite and celebrate the sheer awesomeness of the clue.
Newspaper report:

The unprecedented hype surrounding the mysterious clue has arisen from hundreds and thousands of fans gathering in New York Time's square, where they stand in awe of the clue. Never has this fervent, dedicated crowd been witnessed since Woodstock. Burgeoning from the bridge and tunnel boroughs to Harlem, it is clear that the clue has trolled its very way to the top in celebrating Cluesday. Fans watching these videos of praise come from all walks of life i.e 4chan and greet each other with a rapehug.
by The Clue itself April 28, 2011
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