A Puzzle A Day: 2026-03-24

Correct: 19 hours

Let's analyze the robot's progress: 1. **Net Progress per Hour:** The robot climbs 10 meters up and then slips back 5 meters within the same hour. So, its net upward progress at the end of each full hour is 10 - 5 = 5 meters. 2. **The Common Trap:** A common mistake is to divide the total height (100m) by the net progress (5m/hour), which would give 100 / 5 = 20 hours. However, this doesn't account for the final climb. 3. **Considering the Final Climb:** The trick lies in recognizing that once the robot reaches the top, it has completed its journey, and any potential slipping back is irrelevant. We need to find the point where its next upward climb will get it to the top without needing to worry about slipping. * The robot needs to reach a height of 100 meters. * Its upward climb during an hour is 10 meters. * Therefore, if the robot reaches (100 - 10) = 90 meters, its next climb of 10 meters will get it to the top (100 meters). 4. **Calculating Time to 90 Meters:** To reach 90 meters, with a net progress of 5 meters per hour: 90 meters / 5 meters/hour = 18 hours. 5. **The Final Hour:** At the end of 18 hours, the robot is exactly at a height of 90 meters. * At the beginning of the 19th hour, the robot starts at 90 meters. * During the 19th hour, it climbs 10 meters upwards. This puts it at 90 + 10 = 100 meters, which is the very top of the wall. * Once it reaches 100 meters, it has completed its goal, and the fact that it might slip back during the *remainder* of the 19th hour no longer matters. Therefore, it takes 19 hours for the robot to reach the top of the wall.