Problem 56423. French Conundrum

The French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).
The battle-ground is in a form of a 2-D rectangular lattice spanning from (0,0) to (m,n). In order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position (although relative, consider it to be 0,0) to the end point (m,n).
However, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.
They turn to you, The Army officer and an avid mathematics aficionado to solve the problem.
Given two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.
Solve

Solution Stats

91.67% Correct | 8.33% Incorrect
Last Solution submitted on Sep 19, 2025

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