Math Problem Inquiry Involving nonzero polynomials

[Ben1587]

Find a nonzero polynomial f(w, x, y, z) in the four indeterminates w, x, y, and z of minimum degree such that switching any two indeterminates in the polynomial gives the same polynomial except that its sign is reversed. For example, f(z, x, y,w) = -f(w, x, y, z). Prove that the degree of the polynomial is as small as possible.


No clue how to approach/sove.
Any advice/tips or solutions would be great!

thanks

[matt grime]

the best tip as always is for you to write out some polynomials ans swap over the variables and see what happens and try and find a solution that way