If you’re are an “Olympian” of chem here is how your thought processes should have developed:
As an Olympian you should know that
magnesium burns in air with dazzling brilliance to give MgO and Mg3N2. Hence its use in flash bulbs/flares.
This is multiple choice with only one correct answer;
1.)Magnesium reacted with the nitrogen in the atmosphere to form magnesium nitride
Stop right there! That is the correct answer so mark it as such and move to the next question (two min?). Gives you more time for the difficult questions.
Ignore other considerations they are not relevant. MgO has a high lattice energy (M^2+O^2-; small ions) and hence one of the highest mps known (>2800°C) for an ionic solid, hence its use as a refractory. Does not react with moisture or CO2 in air.
Now only an aficionado will know that MgO2 is difficult to prepare, but you should be able to use your chem intuition to realize that the process MO2 →Δ→ MgO + ½ O2 won’t be prevented at the Ts involved (note huge gain in lattice energy).
I believe Mg5O4 is put there as a subterfuge to distract all but the best students. Ignore it - is a red herring!
Now if they asked what is the fraction of Mg3N2 in the “Mg5O4” sample that is a different matter (answer should take you about 10 mins max).
Ch-Olympian-champion gets part marks.