Imbalance Puzzle - Part 2

Algebra Level 1

The diagram shows how a mobile will be balanced when left to hang, and the rods are all tilted to the maximum degree.

Assuming that the fulcrum is at the center of each rod, what are the relative weights of these shapes?

Rectangle > Triangle > Circle Circle > Triangle > Rectangle Circle > Rectangle > Triangle Triangle > Circle > Rectangle Triangle > Rectangle > Circle Rectangle > Circle > Triangle

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3 solutions

Chew-Seong Cheong
Apr 16, 2015

The left arm: \LARGE{\circ} + > + +\triangle > \square + \triangle \quad \Rightarrow \LARGE{\circ} > >\square

The right arm: + \triangle + \LARGE{\circ} > > \LARGE \circ + + \LARGE \circ > \quad \Rightarrow \triangle > \LARGE \circ

Therefore, > \triangle > \LARGE \circ > >\square

These are interesting puzzles.

There is one detail that is important to actually have these mobiles balance. The balance beams will not balance unevenly as shown if the rods are straight as you have shown. In order to have a balanced beam that works as you have indicated the center fulcrum must be above the two connection points at the ends of the rods when the system is evenly balanced. Straight rods would result in a balancing system where a heavier side would end up directly below the fulcrum, assuming the weights did not contact each otheror the rods.

We can assume the rods are flexing a bit under the strain of the weights or the rods were not straight to begin with to get the results showen

Basicaly;. The length of the right distance of the moment on one side of the balance must be increasing (moving upward) while it decreases (moving downward) on the other side, as the rod is tilted for a ballance beam to work as shown. :)

Darryl Dennis - 6 years, 1 month ago

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Yea the pictures are wrong and probably on purpose, you are simply supposed to use the above logic to get the right answer.

Chris White - 5 years, 7 months ago
Benny Zhang
Apr 29, 2015

This is basically simple algebra represented in a real-life example. Replace the shapes with variables. Let "s" represent the square, "c" for circle and "t" for triangle.

In the first equation (left arm) we have the following, s+t<c+t we subtract 't' from both sides and get s<c

In the second equation (right arm) we have following, c+c<t+c same thing again and this time we get c<t

we combine the two equations and get: s<c<t (square<circle<triangle)

Sr Inco
Nov 11, 2019

{ (Rectangle = x) (Circle = y) (Triangle = z) }

SIMPLE: Rectangle + Triangle < Circle + Triangle
SO: Rectangle < Circle + Triangle - Triangle
THEN: Rectangle < Circle + [ z - z ( value of 0 ) ]
RESULT: Rectangle < Circle


AND

SIMPLE: Circle + Circle < Triangle + Circle
SO: Circle < Triangle + ( Circle - Circle )
THEN: Circle < Triangle + [ y - y ( value of 0 ) ]
RESULT: Circle < Triangle

CONCLUSION:

Rectangle < Circle AND Circle < Triangle
SO: Rectangle < Circle < Triangle
OR: Triangle > Circle > Rectangle

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