Marcus Maths Quiz

[Duggeh]

Theres this 5 question maths quiz on the BBC news website.

http://news.bbc.co.uk/today/hi/today/newsid_7699000/7699177.stm

Anyhoo, if you don't take time to read the questions you'll facepalm yourself at getting them wrong but after 15 minutes of head scratching I still think that question 3 is wrong.

"Imagine picking up a cube with your thumb placed at one corner of the cube and your finger at the furthest corner on the other side of the cube. Now cut the cube exactly down the middle between your finger and thumb. You have two pieces each with a new face. What is the shape of that new face?"

The intuitive answer is square. Cut a cube in half, get a square face. Then you realise that its not a face cut, but a corner cut. This though doesn't change anything because all the sides of a cube are equal, so you get a new face which is square, but larger in surface area than the original 6 sides.

The BBC insists that the answer is a hexagon.

This really threw me, so, I made myself a little paper cube, put my fingers in the appropriate places and then cut it down the proposed line.

Each hollow face section of my paper cube is square. The line they describe does not intersect all 6 faces of the cube. In fact, looking at this cube in my hand, I can't even see a single straight line that will intersect all 6 faces.

Am I missing something here, or is the question just badly written. The others seem fine with a moments thought if you get them wrong.

[Thackary]

They're right - it's a hexagon.

Imagine the cube standing on one corner, with the opposite corner directly above it (so you could spin it on a vertical axis). Now cut horizontally between the two opposite (stationary) corners, and you'll find a line that intersects every face.

[Duggeh]

So the question is badly worded. It should be:

Cut the cube exactly through the middle between finger and thumb, which implies cutting through the equator with the fingers at the poles.

Not

Cut the cube exactly down the middle between your finger and thumb, which implies starting at the finger and moving down that line to the thumb, cutting corner to corner.