How can this problem be reduced to a mathematical one

How can the states of ideal diodes be determined in simple circuits,
with only DC sources and resistors, without a trial and error approach?

I posted this question on Electronics SE and found out that there is none.

This is one of the situations which bugs me that something systematic is going on but I am not able to find it.

For instance:

This in an incredibly simple circuit.
The current has to circulate in certain directions
and only one set of states for diodes satisfy the circulation of current.
It frustrates me to solve this simple problem by guess and check.

Assumption 1

Assumption 2

Assumption 3

Assumption 4

Answer

It looks like solving $2x=5$ by trial and error!

So, what possible approaches can be used,

to analyze this type of circuits in a deterministic manner?

Or at least how can I approach this particular problem in deterministic way?

Hashir Omer
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