avatarBella Lockhart

Summary

The article presents an algebra puzzle involving a series of rings with decreasing diameters, exploring the concept of overlapping lengths to calculate the total length of all rings combined.

Abstract

The puzzle begins with a scenario of rings of diminishing sizes, starting from a diameter of 20 down to 3, and challenges the reader to determine the total length when considering the overlaps between each pair of consecutive rings. The solution provided reveals that there are 18 rings in total, with 17 overlaps, each 2 cm in length. The final calculation accounts for the sum of the outside diameters of all rings, minus the overlaps, resulting in a total length of 173 cm. The article encourages interactive problem-solving, inviting readers to pause and work out the puzzle before revealing the solution. It also fosters a sense of community by asking readers to share their thought processes and engage with the content by commenting and clapping.

Opinions

  • The author believes in the interconnectedness of decisions and their impact on others, drawing a parallel between the puzzle and real-life interactions.
  • The author values reader engagement and encourages active participation in solving the puzzle, reflecting a belief in the importance of learning through practice.
  • There is an appreciation for the aesthetic and visual aspects of problem-solving, as evidenced by the inclusion of diagrams to illustrate the overlapping rings.
  • The author is open to feedback and encourages readers to comment and share their experiences, indicating a desire for a collaborative learning environment.
  • The author seeks support for their work, suggesting that readers buy them a coffee, which shows a personal investment in providing quality content and a connection with the audience.

How Long Are All The Rings?

An Algebra Problem With Many Rings 💍

Perhaps the world is a web of many rings, interconnected and complex. Each one of us is our own ring connected to many other rings. Every minute decision we make will in some way impact another ring very very far away 🦋🌪️

This algebra puzzle involves a series of many rings.

Here’s a hint: what’s the overlap between every two rings …

I recommend you pause the article, grab your pen and paper, and give this a go. When you are ready, keep reading for the solution! ✒️

Solution

First of all, if the first ring is 20 in diameter and the last ring is 3 in diameter. This means there are 20 -3 + 1 = 18 rings in total!

highlighted parts indicate overlap

The second thing to figure out is the number of times the rings overlap. Notice that in the diagram above, there are 4 rings and they overlap 3 times.

1st pair 🪐= 20 and 19 rings, 2nd pair 🪐= 19 and 18 rings, … , 16th pair 🪐= 5 and 4 rings, 17th pair 🪐= 4 and 3 rings

We can extend this reasoning and see that as there are 18 rings in total, they must overlap 17 times.

Finally, the overlap consists of the outer ring of two rings, which are 2 in length in total.

Each ring is 1cm thick

So to put the math together, the required distance is the sum of the outside diameters of the 18 rings minus a 2-cm overlap for each of the 17 pairs of consecutive rings

it’s 173 cm long!

And that’s our answer.

How amazing 👧

What was your thought process this time? Comment down below, I am eager to know :) 💞

Save and share the following list of the best math puzzles on Medium👇

Thank you for reading. Don’t forget to clap the article if you find it insightful.

tip me 💘, i will thank you a million times

I put a lot of effort into writing every article for you, so please buy me a coffee☕ if you are feeling generous. It’s a great way to support my writing as well as my personal and academic life.

Love, Bella ❤️

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