Yijing & Orchestra Conductor

Problem:
The Orchestra conductor has been asked to conduct a series of concert for 2 consecutive months.
The Orchestra has to play few pieces of classical music with the following conditions requested by the organising committee:

1) Play at least 1 piece of music a day;
2) Avoid playing exactly the same music in 2 consecutive days (although partially is allowed)
3) Due to resource constraint, it is impossible to play all pieces of music within a single day.

Question:
At least how many (N) pieces of music the conductor has to prepare in order to fulfill these conditions?

Solution:
Using Yijing （易经）notation:
* a piece of music being played in a day is denoted by
__ (solid line);
while not being played is denoted by
- - (broken line)
* 2 consecutive months in any year have maximum 62 (= 31+31) days.
* A bagua (8 diagramme 八卦) has 64 gua（卦), starting from 6 solid lines stacked on each other (Qian 乾gua) to 6 broken lines stacked on each other (Kun 坤gua), each line (broken or solid line) is called a Yao (爻). 6 Yao makes a gua.
There are total of 64 ($latex = 2^6 $) gua.
* Condition 1) eliminates Kun gua (all broken lines, ie all N pieces unplayed) since at least 1 piece of music to be played in a day.
* condition 3) eliminates Qian gua (all solid lines, sice all pieces can't be played in a single day.
* 64 gua minus 2 above-eliminations left 62 gua.
* these 62 gua have mixture of 6 solid/broken lines, representing 6 played/unplayed combination pieces of
music, with each gua being unique.

=> Answer: The conductor needs to prepare MINIMUM 6 pieces of music.