Why You, Me, and Beyoncé Are All Pigeons

You woke up this morning not expecting to be called a pigeon.

But news flash: mathematically speaking,

you

are

one.

Me? Also a pigeon.

Your mum? Pigeon too.

Welcome to the chaotic, feather-flapping flock.

No, it’s not an insult.

It’s a principle.

The Pigeonhole Principle, to be precise.

We’re all flying around trying to cram into boxes: birthdays, lockers, calendars, cloud storage plans, and math is sitting in the corner smugly whispering, “I told you so.”

And it’s one of the best-kept creative secrets in all of maths.

Maths is so misunderstood.

I’ll happily wave my arms around—front of the classroom, in the pub, or at a fancy dinner party (right when everyone’s in that awkward silence)—and shout, “Maths is one of the most creative subjects!”

Cue the eye rolls.

Cue the side-eye looks like I just claimed I’m a unicorn.

I get it.

Art’s got glitter.

Drama’s got flair.

Music’s got soul.

Maths? Maths has... worksheets.

Maths is where joy goes to get alphabetised.

It’s endless equations, formulas, and doing Exercises 1a) through z) to prove you really get long division.

Sounds about right, doesn’t it?

And yet…

Somewhere between the times tables and the terror of algebra lies this deceptively simple idea that’s secretly brilliant and wildly creative.

It solves problems without actually finding the solution.

No numbers, no scary calculations. Just pure logic — cleverly boxed.

That’s the kind of sneaky elegance you usually find in a Banksy or a jazz solo—saying more with less.

So, here’s the basic idea:

If you try to fit more pigeons than pigeonholes, some pigeonholes are going to double up.

It’s that simple.

But don’t be fooled. Like your toddler’s “innocent” crayon drawings, it gets surprisingly wild once you look closer.

You’ve got more people than seats? Someone’s standing.

More cookies than jars? Someone gets an extra snack.

More Year 9s than chairs in the drama room? Welcome to chaos, brought to you by simple logic.

But wait.

Isn’t that... obvious?

Yes. That’s the trick. It seems obvious.

So obvious, in fact, that you might wonder why mathematicians get so excited about it. But then again, “milk + coffee = latte” also seems obvious, and we still pay £4.60 for it.

It’s not about the simplicity.

It’s about what you do with it.

Because when the Pigeonhole Principle meets creative problem solving, it becomes less about birds and more about brilliantly boxed thinking.

Mathematicians become creative wizards, wielding more clever spells than even Harry Potter could dream of.

In a legendary piece from Mathematical Excalibur, there’s a quote I wish was printed on a tote bag:

“Forming the right boxes is the key to success.”

💡 Let’s pause here: The magic isn’t in the pigeons.

It’s in how you design the boxes.

That’s like saying the creativity of teaching isn’t just delivering the syllabus—it’s in knowing when to turn the whiteboard into a meme wall. Or knowing when to let the kids vote on group names so they feel like they invented algebra.

“Show me this mathematical creativity,” I hear you think.

Here we go...

Pick any 51 numbers between 1 and 100.

Now—prove that at least two of them don’t share any prime factors.

Reckon you start by writing down a choice of 51 numbers?

Let’s be creative instead!

No lists.

No calculator.

No actual prime factor decompositions needed.

The trick?

Use the pigeonhole principle.

If we have 51 numbers (aka ‘pigeons’), we need to design 50 ‘holes’.

Split numbers into consecutive pairs:

(1,2), (3,4), (5,6)... all the way up to (99,100). That gives 50 neat little “holes.”

Now if you pick 51 numbers, one hole must have both numbers. Boom: you've got two that are consecutive (like 35 and 36) and hence can’t share any prime factor.

Simple logic, creative box design. Pigeonhole power level: 🔥🔥🔥

Here’s another one….

Among 9 distinct real numbers, prove there are two numbers a and b such that:

\[ 0 < \frac{(a - b)}{(1 + ab)} < \sqrt{2} - 1 \]

(Yeah, that’s a “Nope!” from most people at first glance.)

That looks... terrifying. Like the kind of thing you screenshot and send to your group chat with “???”.

But we can do this: there are 9 numbers, so we just need to create 8 ‘holes’ for them.

Get creative… get that glitter out, find that soul in the beat, channel your inner drama queen.

What if we turned each number into an angle (using arctan—for the curious). Then divide that range of angles into 8 equal slices. Now each slice is a ‘hole’. Boom: two of your 9 numbers must land in the same slice, meaning they’re close enough to satisfy that intimidating inequality.

Now you’ve got 9 pigeons (numbers), 8 holes (angular intervals)... and the Pigeonhole Principle strikes again, guaranteeing two numbers close enough to satisfy the inequality.

A clever twist of trigonometry and logic.

And honestly? That’s just cool.

Still wondering where this pops up in your life?

Real-Life Pigeons, Real-Life Chaos:

• Teachers, when you shuffle the seating but somehow two kids always end up side-by-side again—pigeonhole magic at work.
• Parents, those 5 kids sharing 2 iPads? At least one is hoarding both and lying about it.
• Students, if 13 of you are in a group chat and there are only 12 months, two of you share a birthday month—statistically cursed to share the cake emoji forever.

Maths always has the ability to surprise us with a hidden beauty

Creative pigeonholing turns logic into strategy. It challenges you to ask:

• What’s the cleverest way to slice the problem?
• How do I turn something messy into a neat set of boxes?
• Can I prove something exists, without ever finding it?

That’s not rote memorisation.

That’s not boring textbook math.

That’s pure, beautiful mathematical mischief.

So yes, you’re a pigeon.

Flying, squawking, squeezing into life’s boxes.

And that’s a good thing.

Because maths isn’t about dull drills — it’s about the clever, creative ways we box up chaos and make sense of the world.

Embrace it. Teach it. Stick it on a mug.

Let the Pigeonhole Principle become your chaotic good superpower. Confuse your enemies. Enlighten your students. Use it to justify your messy kitchen drawer (because clearly: too many spatulas, not enough pigeonholes).

Or just enjoy the moment when a teenager groans, “Ugh, math is everywhere,” and you can gently reply:

“Yes, dear. And so are pigeons.”

Nici

P.S.

If this ruffled a few mental feathers or sparked ideas for your next conversation in the car, wing me an email—I’d love to hear from you. Whether it's questions, creative maths twists, or pigeon puns, I’m all ears.

Because this isn’t just a quirky principle. It’s a mindset. One that proves logic can be creative. It’s playful, surprising, and seriously powerful—and we’ve only just cracked the shell.