Out of Line
Fill in the grid with A-E like a Sudoku. Which letter is in the starred square?
Age
11 to 14
Challenge level
Problem
Image
Fill in the empty squares with As, Bs, Cs, Ds and Es so that no horizontal, vertical or diagonal line contains a letter more than once (including diagonals like the one A and E are on). Which letter goes in the square marked *?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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.
Image
Image
Image
Alternatively, you could use similar logic looking at the second column.