Node-Connection Puzzle

Brain Booster #1

Node-Connection Puzzle

Node-Connection Puzzle

In the figure to the left, suppose you connect each node to every node whose number is less than its own.

Challenge #1: How many total connections would the result contain?

Challenge #2: Suppose there are n nodes instead of 7. Now how many connections will there be?

How This Boosts Your Brain

The first challenge can be solved without too much higher-level thinking (assuming you can make sense of the problem statement); the second cannot. You can solve the first challenge by going node by node, but you have to exercise your faculty of pattern recognition to figure out what happens when the number of nodes is unknown. As with any pattern, you can experiment with a few scenarios (try 5 nodes, 10 nodes, etc.) until you decipher it.

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Solution

Challenge #1: 21

Challenge #2:
n(n-1)
2

What method did you use to solve this challenge? Share your solution method in the comments!


About Jared R

Jared, founder of The Knowledge Roundtable, is passionate about the advancement of knowledge. He has a B.S. in astronomy and physics from UMass and an MBA in Advanced Financial Analytics, also from UMass. He has a day job as a Big Data Analyst in Boston. He has over 500 hours of tutoring experience in everything from algebra to writing. He taught our SAT prep group courses for two years in NH, and before that developed educational content for math, stats, and finance textbooks for two years. His teaching style is hands-on with a focus on problem-solving and critical thinking.

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