My suggestion is: trying to solve it in a conceptual reference frame that is not optimal.
Here is my example. Kleiber’s Law is Max Klieber’s empirical inference that metabolism scales by a 3/4 power of mass. Accordingly, much effort has been invested in trying to deduce a 3/4 exponent from a mathematically based reasoning. An example is the geometric, fracctally based reasoning in A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science , Vol. 276. The 3/4 power relates to energy use. Energy use is the conceptual reference frame. Instead, it appears that a better conceptual reference frame focuses on how much energy distribution capacity increases with increased animal size. In that case, the 3/4 scaling of the rate of metabolism is how evolution responded to the 4/3 scaling of energy supply, to render energy per cell invariant. This is discussed in:
Preprint Size, scaling, and invariant ratios
Preprint From Galileo’s simple case to universal 4/3 scaling
Other examples:
The laws of motion without the concept of inertia (Galileo’s marbles experiments).
The nature of heat without connecting energy, motion and heat.
Equating redshift and luminosity distances for SN 1A. I suspect this is a conceptual reference frame problem.
Do you have other examples?
I browse the Physics help website https://physicshelpforum.com/ Many of the questions posted there appear to be very poorly written homework problems, indicating that the teacher(s) has(have) no idea what they're doing. These problems are often ambiguous and/or missing critical information that perhaps the student is to presume. The problems often are missing units or contain conflicting units. It's a wonder the students learn anything from these pointless exercises. My answer to this topic is: problems that are poorly stated or poorly formulated are hard to solve.
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