The Quipa: The Inca counted everything a conquered tribe owned, everything, down to the smallest thing. They needed a way to remember everything they had counted. To do so, they invented the quipu. The quipu had colored strings tied to a main string. The color of the strings and the distance between the knots tied in each string told a story - how many of this, and what was going on. You had to have special training to be a quipu reader.
Calendar: The Inca invented a calendar they called time makers or time watchers. Time was important to the Inca for religious purposes.
Much More! They also invented a flute, a drum, the famous Inca panpipe (a collection of hollow tubes of various lengths stuck together), terrace farming, aquaducts, hanging bridges, marvelous stonework, dried foods, strange and scary art, a central government, strict laws, a unified language, woven colorful textiles, gold and silver jewelry and statues, wonderful ceramics, specialized professions, a system of communication (the roadrunners) and much more. They were very clever people.
Things they did NOT invent: The wheel and a system of writing