Kavi, the KAVI owl, waving on a book
HomeAcademyAIWho it's forPricingFAQLabsContactGet Started
Math · Stage 4

Use the pigeonhole principle in richer settings

Same worst-case + 1 trick, bigger disguises — months, days of the week, even remainders — plus the leap to guaranteeing THREE of a kind.

✦ Math📘 Stage 4 · S4⏱ ~10 min🧒 Ages 8–9★ Free to start
I can use the pigeonhole principle in richer settings.
Start the free lesson →⬇ Printable PDF
Kavi the owl for Math
📖

Kavi's Birthday Party 🎂

At the party Kavi hoots, "There are 13 of us — I bet two share a birthday month!" There are only 12 months 🗓️. Even on the unluckiest day, 12 friends could each have a different month — but the 13th friend must repeat one. The sock trick grew up: the "holes" aren't colours any more, they're months, days, even leftovers after dividing. Spot the holes, plan for the worst case, then add one!

🎓

What your child will learn

1The holes wear disguisesIn S3 the "holes" were sock colours. In richer puzzles they hide as months, days of the week, or remainders. Your first job is always the same: count how many holes there are. Tap each card.
2Days of the week — the worst-case scoopA week has 7 days, so there are 7 holes. Picture the unluckiest class: the first 7 children born on 7 different days — no shared day yet! Sort these children into day-bins and watch the 8th one land.
3Worst case + 1, any number of holesWrite the guarantee as a number bond. The smallest sure number is the worst case (one in every hole) plus 1. For 12 months: 12 + 1 = 13.
4Guarantee THREE of a kindWhat if you need three the same, not just a pair? The unluckiest grab now fills every hole twice first. With 4 sock colours the worst case is 2 × 4 = 8 socks (two of each, no triple yet) — then one more forces a third. 8 + 1 = 9.
🔍

A peek inside

There are 13 friends at a party. Why must two of them share the same birth month?
holes = 12 months · worst case = one friend per month = 12, still all different · the 13th must repeat → 12 + 1 = 13

Try this at home: There are 12 months. How many people must be in a room to be SURE two share a birth month? 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 4 · S4 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.