Here is one of the mathematic contest problem that my teacher has given me. He said me to solve or find the reason why it cannot be solved. But I was not able to do it. And my searches for similar answers was not effective.
Given: $8 \times 8$ square which consists of 64 squares.
Objective: Draw connected lines from right-bottom square to top-left square which will include EVERY square.
Rules: You must start from right-bottom square and finish at top-left square (See the link). You can only draw a line up, down, left, right directions. Moving diagonally and crossing lines is not allowed.
Sorry for bad English. Please warn me, if you misunderstood the problem. As an example, I provide the solved $7 \times 7$ square with the rules above.