Brain Booster #1
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.
Challenge #1: 21
What method did you use to solve this challenge? Share your solution method in the comments!