[Verse 1]
Picture boxes lined up in a row
You've got one less than the things you need to stow
Eleven pigeons and just ten little holes
Where will they go when the music takes its toll
[Chorus]
Pigeonhole principle, it's mathematical gold
N plus one objects, N containers to hold
At least one box will have two or more inside
There's nowhere for that extra one to hide
Pigeonhole principle, the numbers don't lie
When you've got more things than spaces, some will multiply
[Verse 2]
Thirteen students sitting down for lunch
Only twelve tables in the cafeteria bunch
No matter how you try to spread them out
At least one table gets a doubled route
[Chorus]
Pigeonhole principle, it's mathematical gold
N plus one objects, N containers to hold
At least one box will have two or more inside
There's nowhere for that extra one to hide
Pigeonhole principle, the numbers don't lie
When you've got more things than spaces, some will multiply
[Bridge]
Take it further now, let's expand the rule
K times N plus one, here's the advanced tool
Divide by N containers, what do you see
K plus one minimum, guaranteed to be
[Verse 3]
Twenty-one marbles in just five glass jars
The math tells us exactly where we are
At least one jar will hold five marbles tight
The pigeonhole shows us what's right
[Final Chorus]
Pigeonhole principle, from simple to complex
N plus one objects, now you know what comes next
At least one container will exceed the rest
Mathematics proves it, put it to the test
Pigeonhole principle, the foundation is strong
When objects outnumber spaces, sing along
[Outro]
More objects than containers
Someone's getting extras tonight