Can you solve it? Are you smarter than an Uzbek in 3D?

Can you work out the woodblock puzzle?

Hello guzzlers!

I do my best to bring you the best puzzles I can source from around the world. So far I have brought you puzzles from Japan, Vietnam, Israel and the US.

Today’s challenge comes from Singapore via Uzbekistan.

The woodblock puzzle

Below are the top and front views of a three-dimensional wooden structure.

The top and front views.

Please draw at least one left side view of the structure.

1. in which only wood with flat surfaces is allowed.
   
2. in which wood with curved surfaces is also allowed.
   

Clarifications:

The structure has no painted lines on it.

All edges hidden from view must be drawn as dotted lines. So, the top and front views have no hidden edges.

It is important to remember that the structure is made of wood, which means that no part of the structure can have zero thickness.

To help, I’ll explain why the solution below is incorrect. This object is made from two square pieces of wood, each with a square hole, attached at one edge. At first you might think this is an easy solution … since the top and front views look like those set in the question … but you would be wrong! The trick is to remember the hidden edges, marked here in red.

Incorrect solution. On the left is the view so you can see the three-dimensions. On the right is the side view, which has red dots for the hidden edges.

This object is an incorrect solution because its top and front views will also have dotted lines for the hidden edges, as below. But this contradicts the images in the question, which show that the top and front views have no dotted lines.

The object contains dotted lines for the hidden edges of the wood.

Of course, it is fine for the side view to have hidden edges. But there can be no hidden edges on the top or front views.

Now get solving! The woodblock puzzle really makes you think.

The puzzle is an old one that has been rediscovered by Joseph Yeo, of the National Institute of Education in Singapore, well known to readers of this column as the author of the Cheryl Birthday Problem. He shared the puzzle with Alisher Ikramov, of the National University of Uzbekistan, who he knows from the Singapore and Asian Schools Math Olympiad. Traditionally only the first part is asked, but Alisher has extended it to include curved surfaces.

The solution post is now live.

I post a puzzle here on a Monday every two weeks. If you like this sort of thing check out my other Guardian blog Adventures in Numberland. You can also check me out on Twitter, Facebook, Google+ and my personal website.

If you like gazing at mathematical images and colouring them in, my latest book, Snowflake Seashell Star: Colouring Adventures in Numberland, is out now.

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