Earlier today I set you the following puzzles, designed by the South Korean puzzle master Han Dongkyu. The first two are a slow build up to what is one of the most fiendishly brilliant geometrical puzzles I have ever seen.
If you want a print out of the puzzles, click here.
1. Librarian’s Nightmare Part I
Divide the shape below, which looks like an open book, into two identical pieces. (In other words, if the shape was made of paper, how do you cut it so that you get two identical pieces with no extra material left over. Pieces may be flipped over.)
Now divide the shape into three identical pieces. (Extra puzzle: if you found this too easy, find a second way to cut the shape into two identical pieces.)
Many people saw the ‘simple’ answer straight away. Even so, it is sometimes easy to miss what is hiding in plain sight.
2. Librarian’s Nightmare Part II
Divide the following shape (the book and the hands) into two identical pieces. Again, the pieces may be flipped over.
The hands must coincide, so one of the pieces is flipped. From there it is a matter of using symmetry to cut between them.
3. The king and the castle
Cut the first shape below into two pieces, in such a way that they can be rearranged to make the second shape. The pieces can be flipped.
Han Dongkyu gave the following hints in the pdf document, which you might have worked out by yourself. Although, even with this knowledge, the puzzle still requires astounding spatial reasoning.
1. One of the two pieces completely encloses another piece.
2. The inner piece is shaped like a small dodecagon with some chess pieces attached to it.
3. You can rotate or flip the inner piece to move the rook-shaped hole, for example. A rook attached to the inner dodecagon can fill the rook-shaped hole and leave another hole in its original position
4. What happens if there are more than one rook and king?
I hope you enjoyed these puzzles. I’ll be back in two weeks.
Thanks to Han Dongkyu for today’s puzzles. His website is queuedlab.com
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me. I also give school talks about maths and puzzles (restrictions allowing). If your school is interested please get in touch.
My most recent book is The Language Lover’s Puzzle Book, which is out in paperback this week.