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
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David Price
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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!
Paul Salomon
Lost In Recursion 
Paul,
We exchanged a few emails a while back concerning the look of horizontal lines, whether they are tilted or just look that way. Neither of us could come up with a consistent way of showing this. I thought of using the two lines that denote a 90 degree angle when they are not tilted. What do you think?
Sheldon Lebowitz
Yeah a lot of people think the bars are just in perspective when they first see them, but they just need an explanation. Nothing is in perspective, only tilted. Some puzzles use level bars though and the right angle symbol is smart for that. Good tip!!
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Hi Paul, I am involved with an Open Educational Resource (a free online text). I am wondering if I could include one of these imbalance puzzles in the text. If yes, I would cite you or your blog, whichever you prefer.
My work is under a Creative Commons license. It may be shared or copied for non-commercial purposes, with attribution. Feel free, and thanks!! Please cite me as Paul Salomon and link to my blog.