How many signals would be seen in total in the 13C NMR spectrum
3 different methyl signals: (1, 16) (40, 41) (27, 28, 29, 33, 34, 35)

4 different methylene signals: (17) (2, 15) (3,14) (37, 39)

1 aliphatic CH signal: (36)

2 different aliphatic quaternary C signals: (26, 32) (38)

4 different triple bond C signals: (24, 30) (25, 31) (4, 13) (5, 12)

8 different aromatic carbons: (7) (10) (6, 8) (9, 11) (18) (21) (19, 23) (20, 22)

22 different signals 

Just looked at a model, methyls 40 and 41 are different; one is on the same side of the 6-membered ring as the benzene ring, the other is on the same side of the 6-membered ring as the hydrogen at C-36

23 different signals!