This is a followup project after Singapore International Mathematics Challenge (SIMC) 2018 to calculate the numerical answers to Section C using programming. The simulation is done using C++, while the analysis and graphs are done using Wolfram Mathematica. Also, an analysis of Model 3 of the Champion Team's report (NUSH) was done.

The problem statement may be found in SIMC_Part_C.pdf.

A summary of the results as well as the derivations could be found here.

• Question 3

Attempted to use recursion to solve the problem. For the first and second A, recursion yielded the correct result. Further recursions led to a deviation from simulation results. This may be because when considering events in the recursion, some events may actually not be independent from each other, and hence a more careful approach may need to be used.

• Question 4

The champion team's model involved k lanes instead of 2. For this part, I analysed the distribution of people along the k lanes by dividing the number of people ending at a lane over the total number of people. Except for small values of k, greater values of k always resulted in a spike in probability distribution in the 2nd and (k-1)th row (1-indexed) as compared to the rest of the rows. The 1st and kth row have the lowest probability distribution. Otherwise, the probability distribution is generally equal.

The figure below shows a graph of probability distribution against lane number when k = 10:

The simulation results was fitted to obtain fitting functions. A more quantitative (but very simplified) model was proposed, which models the shape of the general graph quite well.

Project ended on 12/06/2018