Determine Frequency Resolution samples
It's usually considered difficult to resolve a pair of adjacent frequencies unless there is dip between the two FFT peaks.  Depending on the window (rectangular or otherwise) and how much of a dip you require between the two peaks to consider them resolved (above some floor), and whether or what kind of result interpolation you use, you will need from a bit less than double to triple or more of your suggested 800 FFT result bins.

Of course in a-priori zero noise, your signal of 3 pure sinusoids has 9 free parameters, so you might be able to determine your 3 input frequencies with perhaps as few as 9 or a bit more non-aliased samples.  In any case, much less than 800.

The resolution of a single isolated frequency peak above a low enough noise floor to the nearest 10Hz can likely be done using far fewer than 800 samples by using interpolation methods on the FFT result, depending on the SNR.