Step 1: In one full day and night the snail makes a net gain of 3 − 2 = 1 m. Step 2: Do not divide 10 by 1 directly. On the final day, once the snail reaches the top it does not slip back. Step 3: So it must reach 7 m at the end of the 7th night; then on the 8th day it climbs 3 m and gets to 7 + 3 = 10 m, the top. Step 4: Check: the snail climbs to 10 m during the day of day 8, before the night slip happens. Answer: 8 days.