For further clarification, the piece is solid and when it goes through each hole, it touches every point on the inside of that hole.

If you are not used to visualising 3-dimensional shapes, the way to start solving the problem is to first imagine a cylinder of diameter 1 unit. This will fit through the circular hole, touching every point on the inside of the hole.

We will now slice this cylinder until we get what we are after. If we slice a section of this cylinder 1 unit high, the resulting solid will fit through the square hole, since the sideways view of a cylinder 1 unit across and 1 unit high is a square.

The trickiest part of the visualisation is to work out how to get this shape through the triangle, without compromising the circular and square cross sections. This part is done by making two diagonal slices so the triangular cross section is perpendicular to both the square and the circle, as illustrated brilliantly here by Andy Rider, who wins a copy of *Can You Solve My Problems?* because as well as getting the answer correct he included a pun in the solution.

Fruity commendation to Joe Tozer who made the shape out of sliced banana.

If you are still a bit confused, here’s a YouTube clip with a physical example actually going through the holes.