Problem:

Range B2:E6 is a matrix where each cell contains either an \"O\" or an \"X\".
We want to count the number of Xs in each column that are unique in their row (i.e. that particular row contains no other \"X\").

Solution:

Use the SUM, MMULT, TRANSPOSE, and COLUMN functions as shown in the following Array formula:
{=SUM((MMULT(--($B$2:$E$6=\"X\"),TRANSPOSE(COLUMN(B2:E6))^0)=1)*(B2:B6=\"X\"))}
Enter the above formula in a cell under the first column of your matrix (cell B8), and copy it across to the last column.