Unsolvable Seating Arrangement? Investigating the Betweeness of Points Problem

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In summary, the conversation discusses a seating arrangement involving five geometry students: Lee, Linh, Brad, Tiina, and Tammy. They are trying to determine the order of the students based on certain conditions, but there seems to be a discrepancy in the last sentence of the problem. Despite trying different arrangements, they are unable to find a solution without introducing an empty seat. They are seeking assistance in finding a possible solution.
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Moon1
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I have worked for an hour on this - with my mom too. 5 geometry students are sitting in a row. Lee is the same distance from Linh that Linh is from Brad. Tiina is seated between Tammy and Linh. Brad is sitting next to Tiina. Tiina is not seated between Brad a Tammy. What order are they sitting in. We get it to work when Tiina is between Brad and Tammy, but the last sentence makes that incorrect. The only other way we came up with was Tammy, Brad, Tiina, Linh, space, Lee. But I don't think a space is allowed. Not sure what to do next. Thank you.
 
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  • #2
Hello Moon...welcome to MHB. :D

I honestly do not see how such a seating arrangement is possible without introducing an empty seat as well, and I arrive at the same order you did, with an empty seat in the same location.

I would check first to make certain you have the problem written out correctly, with all of the conditions reproduced exactly as given.

But, it is possible that we are missing an arrangement that someone else here may find.
 

FAQ: Unsolvable Seating Arrangement? Investigating the Betweeness of Points Problem

What is the Betweeness of points problem?

The Betweeness of points problem is a geometric problem that deals with finding the point(s) that lie between two given points on a line. It is also known as the midpoint problem or the midpoint theorem.

Why is the Betweeness of points problem important?

The Betweeness of points problem has practical applications in various fields such as engineering, architecture, and computer graphics. It helps determine the coordinates of the midpoint of a line segment, which is crucial in many design and construction processes.

What is the solution to the Betweeness of points problem?

The solution to the Betweeness of points problem is finding the coordinates of the midpoint of the line segment using the midpoint formula, which is (x1 + x2)/2 and (y1 + y2)/2, where (x1, y1) and (x2, y2) are the coordinates of the given points.

What are the properties of the Betweeness of points problem?

The Betweeness of points problem has two main properties: the midpoint property and the segment addition property. The midpoint property states that the midpoint of a line segment is equidistant from the endpoints, while the segment addition property states that the sum of the lengths of two line segments that make up a line segment is equal to the length of the original line segment.

How is the Betweeness of points problem related to other geometric concepts?

The Betweeness of points problem is closely related to other geometric concepts such as the Pythagorean theorem, the distance formula, and the slope formula. It is also used in various geometric proofs and constructions.

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