I saw this problem by Igor Tigerrr Geometerrr, and it has interested me enough that I decided to do this week's problems based on it. Here's the first one, just a bit of a general case to the original problem.
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Here's the second problem inspired by Igor Tigerrr Geometerrr 's post, an extension into 3D.
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New Blog Post! 'Four Fun Math Facts about 2024'
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Three circles packed into an equilateral triangle with side length 4 units. What is the radius of the circles?
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Happy SEVENS day (7-14-2023! YES 2023 is a multiple of 7😉) and here's my 2021 post celebrating Super Sevens!
(Recent updates include heptagon images from the amazing Hana Murray)
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Today's question: Let p be any prime greater than 3. How often will either of the integers p+1 or p-1 be divisible by 6?
#TryMathLive means I'm going to share my thinking here...
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Thus, for EVERY prime p > 3, either p-1 or p+1 must be divisible by 6.
How often? ALL THE TIME.
That was fun! Please share how you thought about it. And check out January Calendar of problems for more #ProblemSolving
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New blog post! March Calendar Problems.
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Igor Tigerrr Geometerrr Fifth problem inspired by Igor Tigerrr Geometerrr 's post, if we start with the tetrahedra where they are in the last problem, but adjust the height so that they are barely touching, find this height in terms of the cube's side length.
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Igor Tigerrr Geometerrr Third problem inspired by Igor Tigerrr Geometerrr 's post, using the same setup as yesterday's problem, the orange pyramid can move around a bit and have an overlapping area with the blue pyramid. Find the maximum area of that overlap.
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Solutions are posted for the April Calendar of Problems! Stay tuned for May calendar later this week...
Also share any of your #ProblemSolving thinking here or on the post!
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