Daily Practice - 11+ Entrance

The same solid (centre stack height 3, all eight surrounding stacks height 2, on a 3 by 3 grid) is lifted, dipped completely in paint so every outward-facing surface, including the underside, is coloured, then rebuilt in exactly the same arrangement. How many individual unit cubes have exactly 1 painted face?

A solid stands on a 3 by 2 grid with heights A1 = 0, B1 = 2, C1 = 1, A2 = 1, B2 = 0, C2 = 3. Which squares are shaded in the plan?

A square sheet of paper is folded in half diagonally, corner to corner, so the bottom-left corner lands exactly on the top-right corner. A hole is punched 2cm from the crease, well inside the folded triangle. How many holes appear once unfolded, and are they the same distance from the crease as the original hole?

Shape 1 is a rectangle 6cm wide and 2cm tall. Shape 2 is a rectangle 2cm wide and 3cm tall. Shape 2's marked 2cm edge joins along part of Shape 1's top edge, flush with the right-hand end. What is the combined shape's height at its tallest point?

Shape A: unshaded triangle. Shape B: unshaded square. Shape C: shaded black pentagon. Shape D: unshaded hexagon. Shape E: unshaded heptagon. Which is the odd one out?