[Daily puzzle] A MSM puzzle \ stacker news ~science

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I stumbled on this nice little puzzle the other day. I'll link to the source tomorrow when sharing the answer. Until then, have fun :)

Find all the possible ways, if any exist, to fill in the three blanks to make all three statements true.

Previous iteration: #726159 (partial proof for special case in #728029)

If you allow words instead of numbers as solutions: odd, irrational, and odd.

Even better than what Randall Munroe had in mind (#731084).

Do the 1, 2, and 3 that label each panel count?

I hadn't thought of that. That way the solution could be something else. Let's give it a try!

▣ 1 = a ▣ 2 = b ▣ 3 = c

a = b + c + 5 b = √(ab3) c = min(a, b , 1)

That's up to you to decide 😜

Trivial solutions are solutions too ;)

There is a unique positive integer solution, assuming we include the panel identification numbers.

x_3 = 1

x_1 = 6 + x_2

x_2 = \sqrt{ 3x_1}

Solving it gives:

x_1=12, x_2=6, x_3=1