This letter attempts to propose explanations for the century-old puzzle which thousands of physicists, including Einstein, Plank, Feynman …have been trying to resolve. A ‘particle’ is first mathematically characterized here as an impulse-function in space; and then Fourier-transformed into wave-number-domain; showing that a ‘particle’ contains a ‘set’ of waves, and not just a single frequency. Then a small ‘set’ of waves is taken and its sum is plotted showing that at most of the places the wave-amplitudes mutually nullify each-other and constructively add only at discrete points in space and time; agreeing with our mathematical characterization. Then we show that in the experiments performed so far the red lasers had at least a few thousand Hz wide line-width; means the sources have been producing a wide set of waves, and not just a pure single frequency. Similarly, in the single-particle interference-experiments incandescent filament-lamps were used with green filters inserted to isolate single photons; but it is obvious that at the frequencies of light very narrow-band-filters are not yet technically feasible, so the green filters used allowed significantly wide band of waves. This wide band of waves passed from both the slits, interfered like waves, and whenever and wherever they got coherently added, a ‘particle’ called ‘photon’ got detected.