double counting – Sumthing Else https://sumthing-else.com Curiosity. Learning. Something more. Wed, 30 Sep 2026 09:20:48 +0000 en-GB hourly 1 https://wordpress.org/?v=7.1.3 https://sumthing-else.com/wp-content/uploads/2026/09/square_public_image-100x100.png double counting – Sumthing Else https://sumthing-else.com 32 32 Counting & Combinatorics – Lesson 6: Clever Counting https://sumthing-else.com/product/counting-combinatorics-lesson-6-clever-counting/ Sat, 26 Sep 2026 02:57:22 +0000 https://sumthing-else.com/?post_type=product&p=2133 Sometimes the quickest way to count something is not to count it directly.

In Lesson 6 of Counting & Combinatorics, learners bring together the ideas from the course and explore a collection of powerful counting strategies.

They investigate counting the opposite, splitting a problem into cases, using symmetry, counting the same thing in two ways and replacing a complicated object with a simpler one.

This lesson includes

  • complementary counting — counting what is easier instead;
  • splitting problems into separate cases;
  • using symmetry to avoid repeated work;
  • double counting and counting the same set in two ways;
  • matching complicated objects with simpler objects;
  • problems involving coin tosses, codes, handshakes, diagonals and subsets;
  • a rectangle-counting challenge;
  • answers and discussion;
  • supplementary exercises for extra practice and revision.

Suitable for learners aged 10 and over. This lesson draws on ideas developed throughout Lessons 1–5.

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This is Lesson 6 of the 6-part Beyond Curriculum: Counting & Combinatorics course.

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