Creating a $4 \times 4$ square grid using $5$ pieces of $8$-inch wires

Question

We would like to create a $4$-by-$4$ square grid using pieces of wire such that the sides of the squares are $1$ inch and we are not allowed to cut the wires. Is it possible to create the grid by using $5$ pieces of wire of length $8$ inch each?

I know that this is not possible, but I am stuck at proving it. I think it is Euler tour related, and the grid itself should contain no Euler tour since there are more than $2$ vertices with odd number of degrees. Any hint on this problem?

Answer 1

Hint:

• How many graph edges do you have available? How many do you need?
• Therefore, how many edges can be doubled?
• Given that restriction, how many wire ends do you need?
• How many wire ends do you have available?