Riddles, one at a time

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.

Which of the four words types the same number as BOOK?

Type BOOK first, then compare each option key by key.

Which row of lamps shows 22?

Start with the biggest lamp value that fits into 22.

Which number from 1 to 99 has the longest Roman numeral, written the usual way?

Which digits need the most letters on their own?

Moving only right or up, how many routes from start to the gem pass the lantern?

Count the ways to the lantern, then the ways from it to the gem, and multiply.

Which tokens pay 18 with the fewest tokens?

Biggest first is not always fewest. Try every pair.