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12/20 23:55 CST Conway and Latham pile on the runs as New Zealand sets the West Indies 462 to win the 3rd test Conway and Latham pile on the runs as New Zealand sets the West Indies 462 to win the 3rd test MOUNT MAUNGANUI, New Zealand (AP) --- Tom Latham and Devon Conway earned a unique place in test history Sunday when their 192-run second innings partnership paved the way for New Zealand's declaration at 306-2 on the fourth day of the third cricket test against the West Indies. Latham made the declaration at drinks in the third session with New Zealand leading by 461 runs. New Zealand earlier had bowled out the West Indies for 420 in reply to its of 575-8, a first innings lead of 155. At stumps after 16 overs the West Indies were 43-0 with Brandon King 37 and John Campbell 2. They will start the last day needing 419 to win on a pitch on which cracks and plates are creating inconsistent bounce. Latham and Conway shared a 323-run opening stand in New Zealand's first innings of 587-8 and became the first pair in tests to achieve a triple century and century partnership in the same match. Conway followed his first innings of 227 with exactly 100 to become only the 10th player and first New Zealander to score a double century and century in the same test. Latham made 137 in the first innings and 101 in the second, emulating his father Rod who joined with Mark Greatbatch to make century opening partnerships in both innings of a test against Zimbabwe in 1992. Meanwhile Kane Williamson, batting first drop, had to wait padded up for more than 86 overs in the first innings and almost 40 overs in the second for his turn to bat. He took advantage of his opportunity Sunday to reach 40 not out. Rachin Ravindra made an unbeaten 46 from 23 balls, rushing as the declaration approached. In the series Conway made 0, 37, 60, 28, 227 and 100: 452 runs at 75.3. Latham made 24, 145, 11, 9, 137 and 101: 427 runs at 71.1. Conway and Latham's partnerships in this test produced 515 runs, more than any opening pair in a single match in all tests. "I think all the work the guys have been doing for a while now is paying off the way they want," New Zealand batting coach Luke Ronchi said. "I think the mindset is where they want it to be and the trust in their own game and the game plans against particular bowlers is coming off. "But it also a nice batting wicket as well, not the traditional sort of New Zealand wicket you see in most test matches. Earlier Sunday, Jacob Duffy took two quick wickets to help New Zealand bowl out the West Indies in the first hour of the fourth day. The West Indies resumed at 381-6 but lost four wickets for 39 runs. Kavem Hodge remained 123 not out, his second test century and highest score. Duffy took 4-86 in the first innings to go with his 5-34 and 3-122 in the first test and 5-38 and 4-86 in the second test: 18 wickets in total at an average of 17.3. ____ AP cricket: https://apnews.com/hub/cricket