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DRY

Code for columns and rows is identical except the board access (board[i][j] and board[j][i] respectively). Such minute difference is hard to spot, and the reviewer (or maintainer) has hard time understanding what's going on. I recommend to factor the common part out, along the lines of:

 bool rowCheck() {
 return boardCheck(rowWize);
 }
 bool columnCheck() {
 return boardCheck(columnWize);
 }
 bool boardCheck(Callable<Integer,Integer> boardAccess) {
 ....
 value = boardAccess(i, j);
 ....
 }

or with lambdas instead of callable wrappers. See this discussion for details.

HashMap

seems like overkill. A bool seen[size] initialized to false and

 value = board[i][j] - 1;
 if (seen[value]) {
 return false;
 } else {
 seen[value] = true;
 }

achieves the same goal with much less overhead. Of course you'd need a bound check.

The side effect of this approach is that your way may have false positives as @CaptainMan noticed in the comment.

DRY

Code for columns and rows is identical except the board access (board[i][j] and board[j][i] respectively). Such minute difference is hard to spot, and the reviewer (or maintainer) has hard time understanding what's going on. I recommend to factor the common part out, along the lines of:

 bool rowCheck() {
 return boardCheck(rowWize);
 }
 bool columnCheck() {
 return boardCheck(columnWize);
 }
 bool boardCheck(Callable<Integer,Integer> boardAccess) {
 ....
 value = boardAccess(i, j);
 ....
 }

or with lambdas instead of callable wrappers. See this discussion for details.

HashMap

seems like overkill. A bool seen[size] initialized to false and

 value = board[i][j] - 1;
 if (seen[value]) {
 return false;
 } else {
 seen[value] = true;
 }

achieves the same goal with much less overhead. Of course you'd need a bound check.

The side effect of this approach is that your way may have false positives as @CaptainMan noticed in the comment.