Daily Math Puzzle: 2026-08-01

A certain distance East of its starting point. — This puzzle plays on how directions work on a sphere, contrasting with intuition developed on a flat surface. Let's trace the probe's path: 1. **North 100 km:** The probe travels along a line of longitude from a lower latitude to a higher latitude (closer to a pole). Let's call the start point A and the end of this leg B. 2. **Turn 90 degrees clockwise, travel 100 km:** From point B, traveling 'East' means moving along the line of latitude at B. Let's call the end of this leg C. 3. **Turn 90 degrees clockwise, travel 100 km:** From point C, traveling 'South' means moving along a line of longitude. Since this leg is 100 km and the North leg was 100 km, the probe will reach a latitude identical to its starting point A. Let's call the end of this leg D. 4. **Turn 90 degrees clockwise, travel 100 km:** From point D, traveling 'West' means moving along the line of latitude at D (which is the same latitude as A). Let's call the end of this leg E. On a flat surface, these four movements (North, East, South, West – all 100 km) would form a perfect square and bring the probe back to its starting point. However, on a sphere, lines of longitude converge at the poles. When the probe travels East for 100 km (from B to C), it does so at a higher latitude (closer to the pole) than its starting point A. Lines of latitude at higher latitudes have smaller circumferences. Therefore, 100 km of eastward travel at latitude B covers a *larger angular change in longitude* than 100 km of westward travel at latitude A (from D to E). Since the eastward segment (BC) resulted in a greater angular shift in longitude than the westward segment (DE), the probe ends up further East than its original longitude. It is at the same latitude as its starting point but shifted to the East.