Well not exactly. Musashi was sunk during the battle of Sibuyan Sea during the Leyte Campaign which occurred on the 24th October 1944 around 10:30 hours. Kurita's Center Force fought the decisive battle on the 25th October morning which is called Battle of Samar. During this encounter Center Force faced off against a motley group of USN escort carriers, destroyers and destroyer escorts. No Japanese ship took critical damage during this particular battle, as the US aircraft and ships present were not particularly well equipped to deal with the massive Japanese Battleships. During this battle Kurita missed his chance of bulldozing through the weak US escorts and engage and destroy the landing crafts at the landing zones (which were his primary targets). It seems that Kurita received a message from SW Fleet HQ that a larger US task force was located only 30 nautical miles from Kurita's present position. It can be presumed that this information effected Kurita's judgment to abandon destroying the weak escorts and attack the landing crafts and to engage the '
real' targets worthy of his fleet; presumably the main US force of Halsey. Kurita broke off the attack and started searching for the Task Force which was nowhere to be found afterwards he turned his force away from the battle zones.
Kurita did not know that Halsey's carriers were lured away from the landing zones by Admiral Ozawa's decoy force so he may have presumed that the Carrier Groups were still present. Later on Kurita himself said "What had we come this far for? Bringing so many ships, and also losing so many ships - wasn't it in order to win a victory at Leyte?" and "I thought it went without saying to steer towards the enemy force that was stronger." Perhaps he did not consider the landing crafts worthy targets?
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Image of Yamato, Musashi and other ships of Center Force being attacked during the battle of Sibuya Sea.
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USS Essex struck by Lt. Yoshinori Yamaguchi's special attack D4Y3 Model 33 aircraft, at 1256 hours on 25 Nov 1944, photo 07 of 10
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Yamato hit by a bomb in Sibuyan Sea, 24 Oct 1944