[chidevguy]

I was able to get 2048 building off of your solution. As you said, always keep your highest number in the top right corner. Try to build the next highest numbers up along the right edge, so that you have say, 256, 128, 64, 32 along the right edge. Always keep 4 numbers there, and only use up/down/right. Then just focus on building whatever number you need next to double the bottom right number, so that you can "chain up" numbers along the right edge and double your highest number in the top right.

Kind of hard to explain in words, but hopefully that helps!

[pedrocr]

Yep, this is pretty much the same solution with the right edge instead of the top edge. I got to 1024 and then blundered and couldn't get 2048. This thing is addictive though.