Equilibrium energy — UPSC Physics Optional CSE 2013 Paper I

N particles obeying Classical Statistics are distributed among three states having energies \varepsilon_1 = 0, \varepsilon_2 = k_{\mathrm B}T and \varepsilon_3 = 2k_{\mathrm B}T, where k_{\mathrm B} is Boltzmann constant. If the total equilibrium energy of the system is 1000k_{\mathrm B}T, calculate the value of N.