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Math · Stage 3

Smallest number that GUARANTEES it

To be 100% sure, plan for your unluckiest day — picture the worst case, then add one. That is the pigeonhole principle.

✦ Math📘 Stage 3 · S3⏱ ~10 min🧒 Ages 7–8★ Free to start
I can find the smallest number that guarantees an outcome by reasoning about the worst case and adding one (the pigeonhole principle).
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Kavi the owl for Math
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Kavi's Dark Sock Drawer 🧦

The lights are OUT and Kavi's drawer mixes socks of 5 colours 🧦. "How many must I grab to be GUARANTEED a matching pair?" Kavi imagines the unluckiest grab — one of every colour, 5 socks, still no pair! But the very next sock must repeat a colour. So 5 + 1 = 6 socks are certain. The trick is never to count on luck — plan for the worst case, then add one!

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What your child will learn

1"Maybe" vs "Must""To be sure" is a strong word. A lucky grab might work — but a guarantee has to work every single time, even on your worst day. Tap each card.
2The unluckiest scoopPicture the unluckiest grab from a 4-colour drawer: one of every colour first — 4 socks, still no pair! Each dot shows a sock’s colour. Sort these five socks into colour bins and watch the 5th one land.
3Worst case + 1Write the guarantee as a number bond. The smallest sure number is the worst case (one of every kind) plus 1. For 5 colours: 5 + 1 = 6.
4The + 1 never stopsLine up colours and their sure numbers. Each guaranteed answer is just one more than the number of colours: 2→3, 3→4, 4→5, 5→6, 6→7.
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A peek inside

Socks come in 5 colours in a dark drawer. How many must Kavi grab to be GUARANTEED a matching pair?
worst case = one of each colour = 5 socks, still no pair · the next one MUST repeat → 5 + 1

Try this at home: Socks come in 3 colours in a dark drawer. How many must you grab to be sure of a matching pair? Why?

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

Start the free lesson →⬇ Download PDF

Part of Math · Stage 3 · S3 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.