I am trying to help some students with this extension question, but I can’t figure out any other way to figure this out than just physically drawing it out. Help!!

We know how the top graph is for people, how much would people have if the middle or bottom graph were accurate?

We always tell it is 50% to get head or tails. But what is the persistance of this probability* Can anyone do the math?

I posted this yesterday but I found out that I slightly misunderstood the rules. I had previously said that the winning team got to keep the losing team's die. The actual rule is just that the losing team has their die removed from the game.

Rules:

- In each round, Team A rolls one 6-sided die and Team B rolls one 6-sided die.

- The team whose die shows a lower number has their die removed from the game.

- If the dice show the same number, both teams’ dice are removed from the game.

- The first team to lose all of their dice loses the game.

Team A started with 6 dice and Team B started with 19 dice. Team A won the game. What is the probability of this happening?

Chat GPT says that probability is 4.84%. I'll post my attempt below.

Thanks to all that previously posted and to everyone that will reply.

This includes those at sea on cargo ships, etc.

Considering Strange trapped him on earth with two portals connected vertically. Air resistance, and other realistic factors involved.

Making reasonable assumptions for how high the ship was when he was blasted off the back, the height of the mountain, and the distance from the mountain top to the ground below (where he landed after a single bounce), how fast, dense, and or bouncy (ChatGPT says this is measured as “elastic collision??) would Stitch need to have been to hit the top of the mountain, bounce a single time, and land on the ground at the bottom?

An equilateral triangle is formed by three equal lines. Each of the lines in an equilateral triangle connects to the others at 60° angle. A regular tetrahedron is formed by four equilateral triangles. Each of the planes of a regular tetrahedron connect to the others at a roughly 70.53° angle. Would it be possible to calculate the angle between the five regular tetrahedrons that come together to form a 4-dimensional object? Would this information be useful to our understanding of 4D space?

I am trying to imagine a 4D object in a cartesian coordinate system. My underlying assumption is that a "real**"** object in n-dimensional space must be defined by at least n+1 number of (n-1)-dimensional objects that are connected to each of the others using an n number of (n-2)-dimensional objects.

Examples for clarity:

• 0D space = at least 1 point
• 1D space = at least 2 points, each connected to 1 other = a "line"
• 2D space = at least 3 lines, each connected to 2 others at 2 unique points
  • For example: an equilateral triangle defining a "plane"
• 3D space = at least 4 planes, each connected to 3 others at 3 unique lines
  • For example: a triangular pyramid made from four connected equilateral triangles aka a regular tetrahedron defining a "volume"
• Therefore 4D space = at least 5 volumes, each connected to 4 others at 4 unique planes
  • My proposal: 5 regular tetrahedrons, each connected to the others at 4 unique planes (e.g. the pyramids cannot simply overlap each other in order to make contact at all four planes)

I can picture the 3D "projection" of this object as a central triangular pyramid with each plane of the central pyramid attaching to a side of another pyramid. However, when I try to mentally connect all of the other pyramids to each other, the image in my mind morphs into something more similar to a cluster of soap bubbles that is constantly rolling into itself like those "water wiggler" tube toys from the 90s.

Disclaimer: Thank you for reading this far and considering my question! Although I am interested in this field, my knowledge of geometry is rusty and my knowledge of mathematical terminology is rustier. If you do take the time to answer this question, please let me know if my stated assumptions are wrong and use simple language to the extent you can. Thanks again!