The sum of sigma $$(\sigma)$$ and pi$$(\pi)$$ bonds in Hex-1,3-dien-5-yne is _______.

We consider Hex-1,3-dien-5-yne, whose structure is $$CH_2=CH-CH=CH-C\equiv CH$$, a six-carbon chain with double bonds at positions 1-2 and 3-4 and a triple bond at positions 5-6.

For $$\sigma$$ bonds, there are C-C single bonds between C2-C3 and C4-C5 (2 $$\sigma$$), one $$\sigma$$ each from the two C=C bonds at C1=C2 and C3=C4 (2 $$\sigma$$), and one $$\sigma$$ from the C≡C bond at C5-C6 (1 $$\sigma$$), giving a total of 5 C-C $$\sigma$$ bonds. The C-H bonds contribute $$\sigma$$ bonds as follows: C1 has 2H, C2 has 1H, C3 has 1H, C4 has 1H, C5 has 0H and C6 has 1H, totaling 6 $$\sigma$$ bonds. Hence the overall $$\sigma$$ count is 5 + 6 = 11.

Each double bond has one $$\pi$$ bond, so the two C=C bonds provide 2 $$\pi$$ bonds, while the C≡C bond provides 2 $$\pi$$ bonds, for a total of 4 $$\pi$$ bonds.

Therefore, the molecule contains $$\sigma + \pi = 11 + 4 = 15$$ bonds in total.