The Lamp and the Wall
Read the puzzle
A lamp shines across cubes stacked on a 4 by 4 base toward a wall. Facing the wall from the lamp side, the four rows run left to right; each row's stack heights, from lamp to wall, are: row 1: 1, 0, 1, 2; row 2: 0, 1, 2, 3; row 3: 0, 1, 0, 0; row 4: 1, 1, 2, 0. Each shadow option is four columns, heights left to right: A 3-2-1-1, B 2-3-1-1, C 2-3-1-2, D 2-2-1-2. Which shadow appears on the wall?
Which shadow appears on the wall?
C
Each row's tallest stack sets the shadow.
How to solve it
The light travels along each row toward the wall, so every row casts one column of shadow. A cube hidden behind a taller one adds nothing, so a row's shadow is only as tall as its tallest stack.
Step one: find the tallest stack in each row. Row 1 has stacks of 1, 0, 1 and 2, so its column is 2 high. Row 2 has 0, 1, 2 and 3, so 3 high. Row 3 has a single cube, so 1 high. Row 4 has 1, 1 and 2, so 2 high.
Step two: read the shadow left to right: 2, 3, 1, 2. That is shadow C.
The usual wrong answer is B (2, 3, 1, 1). It comes from judging the last row by the low cubes at the front and missing the 2-high stack further back, nearer the wall. A, with its tall 3 on the far left, comes from mixing up which row holds the tallest stack.
Quick check: the tallest stack in the drawing is three cubes, so exactly one shadow column must reach 3. D has no 3, so it fails at once, and A puts its 3 in the wrong column.
