[Verse 1]
Twenty students, fifteen desks to fill
Someone's sharing, that's the natural drill
When abundance meets a smaller space
Overlap becomes the commonplace
Pigeonhole principle sounds so neat
But choosing wisely makes the theory complete
[Chorus]
More pigeons than the holes can hold
Collision's guaranteed, the math's been told
Pick your objects, pick your bins with care
The magic happens when you know what pairs
Abundance forces, overlap's the game
Different choices make the power's name
[Verse 2]
Seven colors painting rainbow's arc
Fifty pixels make some shades remark
Two must share the spectrum's limited range
Birthday paradox feels rather strange
Twenty-three people in a crowded room
Two share dates, dispelling birthday gloom
[Chorus]
More pigeons than the holes can hold
Collision's guaranteed, the math's been told
Pick your objects, pick your bins with care
The magic happens when you know what pairs
Abundance forces, overlap's the game
Different choices make the power's name
[Bridge]
Trivially obvious, the concept seems
But applications burst beyond our dreams
Hash tables buckets, network packet streams
Computer science built on overlap schemes
The art lies not in proving what must be
But crafting categories strategically
[Verse 3]
Infinite numbers, finite memory blocks
Some addresses host more than one box
Passwords hashing to the same location
Proves that smart design needs calculation
Choose your pigeons, choose your holes with thought
Simple principle, complex battles fought
[Outro]
When abundance meets constraint's embrace
Collision's certain in that bounded space
The power's hidden in the choice you make
What to count and how the groups you break