## To determine if it is possible to arrange 5 coins so that every coin touches every other coin, you need to consider the geometry of the situation. One approach is to draw a diagram or use a physical representation to visualize the possible arrangements.

A helpful resource for understanding such arrangements is a math concept called graph theory, specifically the concept of a complete graph. In a complete graph, every vertex (representing a coin) is connected to every other vertex (coin) by an edge. In this case, the edges between the coins would represent the touching points.

Using graph theory, we can determine that a complete graph with 5 vertices requires 10 edges. Each coin can connect to 4 other coins, but since the coins cannot be stacked or overlap, they can only touch each other at a single point.

Drawing the possible arrangements, you will find that it is not possible to arrange 5 coins so that every coin touches every other coin if they lay flat on the table and no stacking is allowed. This is because a complete graph with 5 vertices would require 10 edges, but only 5 points of contact are available when the coins are laid flat.

To visualize and understand this concept better, you can refer to the provided link to a lecture on complete graphs in graph theory.