Superpermutations - Numberphile
The Great Courses Plus (free trial): http://ow.ly/C3FE30hIvhc This video features Dr James Grime. More links & stuff in full description below ↓↓↓ More James Grime on Numberphile: http://bit...
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[James]: Not just regular permutations, super-permutations, “can leap tall buildings in a single bound” permutations. What is a super-permutation? First of all let’s talk about an ordinary permutation. A permutation is just like a shuffle, so imagine I had three cards: 1, 2, and 3. How many ways can I shuffle those three cards, so let’s do that? These are the permutations: 1,2,3, and we could have 1,3,2, 2,1,3, 2,3,1, and we could have 3,1,2 & 3,2,1. There are six permutations that use the numbers 1 to 3, and that is three factorial (“3!”). Just to remind people, 3 factorial means 3×2×1, and that’s because we've got three choices for the first one, two choices for the second one, and one choice for the last one. And you mult...
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[James]: Not just regular permutations, super-permutations, “can leap tall buildings in a single bound” permutations. What is a super-permutation? First of all let’s talk about an ordinary permutation. A permutation is just like a shuffle, so imagine I had three cards: 1, 2, and 3. How many ways can I shuffle those three cards, so let’s do that? These are the permutations: 1,2,3, and we could have 1,3,2, 2,1,3, 2,3,1, and we could have 3,1,2 & 3,2,1. There are six permutations that use the numbers 1 to 3, and that is three factorial (“3!”). Just to remind people, 3 factorial means 3×2×1, and that’s because we've got three choices for the first one, two choices for the second one, and one choice for the last one. And you mult...
