Climbing Robot
Read the puzzle
A robot starts at the bottom of a 10 m wall, marked from 0 m to 10 m. Each day it climbs up 3 m, and each night it slips back down 2 m. On which day does the robot reach the top of the wall?
A robot climbs a 10 m wall. Each day it climbs 3 m; each night it slips back 2 m. On which day does it reach the top?
On the last day it does not slip back.
Day 8
After night 7 it is at 7 m; day 8 takes it to 10 m.
How to solve it
Track the height at the end of each day and each night, and stop the moment the robot reaches 10 m.
Over a full day and night it gains 3 − 2 = 1 m. So after night 1 it is at 1 m, after night 2 at 2 m, and after night 7 at 7 m.
On day 8 it climbs from 7 m to 7 + 3 = 10 m, which is the top. It never slips back that night, because it has already arrived.
The usual wrong answer is day 10, from dividing 10 m by the net gain of 1 m per day. That method assumes the robot slips every night, including after the final climb. Once it is within 3 m of the top, a single day's climb is enough.
A cleaner way to see it: the robot must start some day at 10 − 3 = 7 m or higher. Gaining 1 m per full cycle, it reaches 7 m after 7 nights, so the climb that finishes is on day 7 + 1 = 8.
Quick check: on day 7 it goes from 6 m to 9 m, which is still short of 10 m.
