4 months ago, thinking on balance puzzles like these, I started wondering about problems of imbalance. “What if the scales tip?” I thought, “what information do we get, and how can I use it to make a good puzzle?” I wrote fifteen imbalance puzzles of my own, but I took things further and offered prizes to my two favorite imbalance puzzle writers. In the math section above, I put together a page including my puzzles and the contest submissions. You should take a look, because there are LOTS of good submissions.

BUT four months is plenty, and it’s time to announce winners. Congratulations to Nathan Chow and David Price who I’ve selected as my favorite puzzlists!!! Based, as I said, on “incredibly subjective criteria,” I chose these two for the way that they extended the state of the art. Their problems really stretched my ideas into wonderful new territory. THANKS BE TO THEM!

#### “Entangled Imbalances” by Nathan Chow

#### David Price

As promised, Nathan and David each win a print of their choosing from my Stars of the Mind’s Sky series, up to 13″x 13″. All of the rest of us get to solve these wonderful puzzles.

**Honorable mention** goes to Felix, a fifth grader I got to work with last year. Felix is a wonderful young mathematician, and he came up with a really nifty imbalance problem. I don’t want to spoil it for you so solve now, and I’ll continue below.

#### Felix (5th grade)

SPOILER: Felix started with the idea that his puzzle would include negative weights, which really tickled him. I think he reveals the information really nicely in the puzzle. Thanks, Felix, for the wonderful puzzle!