Their position was more dire because wicketkeeper Shane Dowrich could not bat in either innings because of a broken finger and they have only nine wickets.
But Blackwood and Joseph combined in an unbroken partnership which broke the dominance of the New Zealand bowlers and was worth 107 runs at stumps.
While New Zealand still lead by 185 runs, the seventh-wicket pair brought respectability to an otherwise bedraggled West Indies performance.
Blackwood, the West Indies' last recognized batsman, led the stubborn resistance and was 80 not out at stumps, having hit nine fours and two sixes.
Joseph, attempting to establish himself as an allrounder, achieved his maiden test half century and was 59 not out.
The pair played aggressively and managed to hit the New Zealand bowlers off the lengths which had been so successful throughout the day. Their 100 partnership came up from only 111 balls. The New Zealand vs West Indies Test series is also a part of ICC World Test championship.
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