[Verse 1]
Five dots scattered in a perfect square
You claim they'll spread without a care
But slice that space in quarters neat
Watch the math make your claim retreat
Thirteen friends around the table
Birthday months? The odds aren't stable
Twelve slots filled by thirteen souls
Something's gotta break the molds
[Chorus]
Too many pigeons, not enough holes
The numbers always tell their roles
When objects crowd the sorted space
Collision's written on their face
Count the items, count the bins
Mathematics always wins
Pigeonhole will find the match
What you scatter, logic'll catch
[Verse 2]
Take a sequence, long and strange
Real numbers in their random range
If n-squared plus one's your count
A pattern's bound to surmount
Erdős-Szekeres knew the trick
When sequences get thick
Either climbing up or sliding down
A monotone path will be found
[Chorus]
Too many pigeons, not enough holes
The numbers always tell their roles
When objects crowd the sorted space
Collision's written on their face
Count the items, count the bins
Mathematics always wins
Pigeonhole will find the match
What you scatter, logic'll catch
[Bridge]
Divide and conquer, split the domain
Watch repetition stake its claim
Maximum distance, root-two-halves
When geometry does the math
From birthdays to sequences long
The principle stays strong
[Final Chorus]
Too many pigeons, not enough holes
Overlapping's in their souls
When the count exceeds the space
Duplicates will show their face
Simple counting, profound might
Pigeonhole cuts through the night
What seems scattered, what seems free
Hides its inevitability
[Outro]
Thirteen people, twelve months time
The collision's paradigm
Five points dancing in their square
Two will meet, it's always there