Recently we have reported the Γ n / Γ p value, ∼0.5, obtained in the exclusive coincidence measurement of the nucleon pairs in the back-to-back kinematics, which led to the resolution of the long standing Γ n / Γ p puzzle. We also have reported the branching ratio of the three-body process in the nonmesonic weak decay of 12 ΛC to be 0.29 ± 0.13 by reproducing the quenching of the nucleon yields. At the same time we have finally obtained the absolute decay widths Γ n and Γ p taking account of the three-body processes. However, there still are serious inconsistencies not only between the experimental and theoretical values of important observables such as the decay asymmetry parameter α N M , but also between the basic formalisms of theoretical models. In order to provide more stringent guides for theoretical models, it is urgent to measure the fundamental observables, such as Γ n , Γ p , and Γ 2 N , with much improved accuracy. In this regards, the next extensive coincidence experiment is planned at the J-PARC 50GeV PS for the accurate determination of the decay widths to the level of ∼ 10 % statistical uncertainty and the measurement of Γ 2 N in the exclusive way.