In the standard double-slit experiment, the interaction between the electron and a detector at either of the slits is supposed to be local. However, one never notices a situation where the electron is detected at both slits simultaneously in the frame of the observer. This is usually explained by the statement that there is only one electron that is being located and it obviously cannot actually be located in two places at the same time in the observer's frame of reference. However, this is a global constraint, which is hard to understand when the interaction between the electron and a measurement device at a particular slit is completely local - how would the measuring device realize that there was only one electron that was to be detected? It would be useful to deduce this from purely local interactions at each slit, even with detectors at each slit, without having to adduce assumptions about long-range correlations between (potentially) space-like separated events. In this paper, we start with a Hamiltonian that was studied in a previous paper on the measurement problem, with a local interaction between the electron and a detector - here we assume that there is a detector at each slit. We study this problem numerically and also make a theoretical argument that the detection problem is exactly the same as that of the problem of equilibration of a macroscopic number of coupled harmonic oscillators. At each detector, as the measurement happens, the amplitude for each of the states of the measuring apparata relaxes to an equilibrium configuration akin to the equilibration of a thermodynamic system. The problem of the detection of the electron at each slit is then mapped to the motion of a random walker in a line with reflecting barriers at both ends, where the ends are separated by a macroscopic number of steps. This connection to a well-studied mathematical problem has a well-understood consequence - two (or a finite number of) random walkers in this space will be expected to be separated by a macroscopic number of steps. Hence, only one of the detectors will see a macroscopic number of its detection degrees of freedom affected - ergo, only one of the detectors, selected completely at random, will "see" the electron. For a large, macroscopic, though finite-sized measurement device, there will be a vanishingly small chance of detecting the electron simultaneously at both slits. Indeed, in the limit of an infinitely massive detector, we will never detect the electron at two places at the same time. This problem also illustrates further that the systematic application of Schrödinger's equation along with a local interaction Hamiltonian that effectively represents the measurement process helps solve some curious issues in the quantum measurement problem.