This is from wiki, so it may not be 100% accurate. Still looking for info that confirms more torp/bomb hit count as confirmed that may be higher... but this is what I found, thus far:
From the first attack at 12:37 to the explosion at 14:23, Yamato was hit by at least 11 torpedoes and 6 bombs. There may have been two more torpedo and bomb hits, but this is not confirmed.
M. M.
That article does mention of a lot of near misses by bombs that could have contributed to the damage suffered by the Yamato, that ultimately led to its demise... as well as some believed to be, yet not able to be confirmed hits by torps... which could bring it up on the total # that did hit to what Bubblehead alluded to.