Subcategories

• M0 Introduction

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  I know another way which is basically the same and the why. So it is just base x height divided by 2. The base of a square for example can be 4. Then the height of the square (the length) can be 3. Cutting a square in several pieces it is possible to get a triangle. Triangles are contained in any polygon.

• M1 Algebra Basics

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  D-1 is not quite intuitive to me, I wonder why it is 1 and what 1 represents.
  if it refers to how we picture the slower runner is at speed 0 and only count the relative speed that is produced by the faster runner, why it is 1 then?

• M2 Geometry Tools

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  Hi! This is in relation the question at the end of this explanation. I'm confused about how angle CGH can be inscribed to arc CG. Could someone help explain? Thank you 🙂

• M3 Combinatorics Tools

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  The way I did it, and I thought he would too, was by considering the possible placements of B for any place of A. Since after we have defined 2 of the 4 elements, the other two can only be arranged in two ways. Then, you can add up all the ways to put A before B with considering the other two elements as one singular one, and then multiply by 2.
  So, with A in front 3 placements work, second, 2 and so on, so that we get 3+2+1=6. Then, we multiply by 2 to get 12.
  this also works on the your turn, except that there is actually only 1 arrangement of C and D for every placement of b.

• M4 Algebra Tools

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  @wisegiraffe I got this too first, but I noticed it tricked me. You add four of the same variables and subtract one of the same variable, so you get 3

• M5 Number Theory Tools

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  The reason that the greatest possible sum of A, C and E is 6 instead of 9 is because of the limitation that A+C+E=B+D. Since the greatest value B and D can be is 3, the maximum value that the sum of B+D can be is 6.

  If you set A,C, and E = 3; you'd basically say 3+3+3 = 9 = B+D, which isn't possible since the max of B+D is 6 and 9 > 6.

• Practice Mini-Courses

  Workout 1A (Algebra) Workout 1B (Algebra) Workout 2A (Geometry) Workout 2B (Geometry) Workout 3A (Combinatorics) Workout 4A (Algebra) Workout 5A (Number Theory)
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  Since 2021=2025-4=45^2-2^2, which means that 2021 can be written as (45+2)(45-2)=43*47. It's more faster than guessing the numbers and it's more easy to memorize. Although not all numbers can be solved that way