🍬 Sharing the Candy

Explore integer partitions — how many ways can you split a number into groups?

10
42
Total partitions
10
Distinct parts
10
All odd parts
Notice: distinct parts = odd parts. Always! Why?
🫘 Jelly Bean Lab
📋 All Partitions

Drag jelly beans into groups to build partitions. Can you find them all?

Unassigned beans (drag from here):
Groups:
+
Place all beans into groups to make a partition
Your discoveries: 0 / 42

Click any partition to see its Ferrers diagram. Underlined = all different sizes (like the textbook!).

⬤ Ferrers Diagram
📊 Discovery Table

A Ferrers diagram shows a partition as rows of dots. Flip rows↔columns to see the conjugate.

Select a partition

This table summarizes the partitions — just like the textbook's analysis on page 115.

Explore & Discover

  • For n = 10, there are 42 partitions. How many for n = 11? Can you predict without listing them all?
  • The number of partitions with ALL DISTINCT parts always equals the number with ALL ODD parts. Can you see why using Ferrers diagrams?
  • What happens to the number of partitions as n increases? Does it grow fast or slow?
  • If you flip a Ferrers diagram (conjugate), what partition do you get? When is a partition its OWN conjugate?
  • For n = 100 (the textbook's challenge), there are 190,569,292,356 partitions. That's a LOT of jelly beans!