The starred square contains a B.

The square marked in yellow in the diagram on the right must be a D, since it is in the same row as B and E, and the same column as A and C.

The square marked in yellow must contain a B, as it is in the same column as A, D and B, and is in the same diagonal as E.

Consider the top row. This must have one of each of the letters in it, so in particular it must contain a B. The right-hand-most square is in the same column as the green B. The square to the left of this is in the same diagonal as this green B. The left-hand-most square is in the same diagonal as the black B. This means only the yellow square can contain the B.

Alternatively, you could use similar logic looking at the second column.

The square marked in yellow in the diagram on the right must be a D, since it is in the same row as B and E, and the same column as A and C.

The square marked in yellow must contain a B, as it is in the same column as A, D and B, and is in the same diagonal as E.

Consider the top row. This must have one of each of the letters in it, so in particular it must contain a B. The right-hand-most square is in the same column as the green B. The square to the left of this is in the same diagonal as this green B. The left-hand-most square is in the same diagonal as the black B. This means only the yellow square can contain the B.

Alternatively, you could use similar logic looking at the second column.

*This problem is taken from the UKMT Mathematical Challenges.*