Daily Math Puzzle: 2026-06-21

2 — A shortest route from (4,1) to (1,4) requires 3 north moves and 3 east moves, i.e., 6 steps. Without obstacles there are C(6,3)=20 such routes. Count the routes that hit a pillar and subtract them. - Through (1,2): 4 ways. - Through (2,4): 10 ways. - Through (3,1): 10 ways. - Through (4,3): 4 ways. Total single‑pillar routes = 28. Some routes pass through two pillars (they are counted twice above, so add them back): - (4,3) → (2,4): 3 ways. - (3,1) → (1,2): 3 ways. - (3,1) → (2,4): 4 ways. Total double‑pillar routes = 10. No route can pass through three pillars because the required north/east ordering breaks down. Using inclusion‑exclusion, bad routes = 28 − 10 = 18. Good shortest routes = 20 − 18 = 2. Thus there are exactly **2** distinct shortest paths that avoid all pillars.