Imbalance Problems

Balance problems are all too common, and we’re all away aware of their connection to systems of linear equations.  But, what if the scales don’t balance?  What if one side weighs more?  Behold, my “imbalance problems.”

In each case, order the three shapes by weight

Imbalance 1 Imbalance 2 Imbalance 3
Imbalance 4 Imbalance 5 Imbalance 6
Imbalance 7 Imbalance 8 Imbalance 9
Imbalance 10 Imbalance 11 Imbalance 12
Imbalance Problem 13 Imbalance Problem 14 Imbalance Problem 15

Contest Submissions

I offered a prize for great imbalance problems.  My favorite two puzzlists won a print of their choosing from the Stars of the Mind’s Sky series, up to 12″x12″.  You can see the submissions below.


“Entangled Imbalances” by Nathan Chow

Entangled 1 Entangled 2 and 3

David Price

David Price David Price 2
David Price 3 David Price 4

Honorable Mention

Felix (5th grade)

Felix's imbalance

More great submissions

“Infinite Imbalances” by Harvey Johnson (see his blog post)

Infinite Imbalance 1 Triple Helix Imbalance Infinite Imbalance 3

David Millar

David Millar 1 David Millar 2


Christopher Danielson

Chris Harrow

Mayya_subtilis imbalance Christopher Danielson 1 Chris Harrow

Geogebra Applet by John Golden

John Golden's Geogebra applet


2 responses to “Imbalance Problems

  1. sheldon lebowitz

    Sometimes freehand drawings don’t quite show if there is an imbalance or just a perspective problem. Could you amplify on this point?

  2. So cool! I just grabbed a screenshot so I could post them all to pinterest. Thanks for creating this (I’m printing now and probably won’t get squat done until I finish them!).


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