Hello guzzlers,

Scalpels at the ready! Today, three dissection puzzles.

1. Can you cut the shape below into two identical parts using one single line? The line does not have to be straight.

This jagged geometrical brainteaser is from the vault of American science writer Martin Gardner, who died in 2010. The Gathering for Gardner Foundation, an organisation founded in his memory, runs an annual event called Celebration of Mind in which people are urged to get together and play mathematical games. The events are usually on or around October 20, which was Gardner’s birthday. You are all taking part just by reading this column…

2. Here’s another Gardner classic. Below are two figures, each divided into four parts that are all identical in shape. Can you divide the square into five parts that are also all exactly alike?

3. The Yin and Yang symbol below is a large circle divided into two equally-sized regions, one black and one white. The outline of each region is made from three semi-circles, a large one, and two smaller ones of equal diameter. The diameter of the small ones is exactly half the diameter of the big one.

Your challenge is to cut the Yin and Yang into two with a single line, such that the areas of the black and the white regions are both equally split in two. The simplest way is with a non-straight line. But it’s also possible with a straight line. Can you find it?

The Yin and Yang puzzle was devised by Henry Ernest Dudeney [1857-1930].

I’ll be back with the answers at 5pm UK time today.

NO SPOILERS PLEASE. (Although since you can’t post images below the line, these puzzles are almost spoiler-proof) Instead discuss Martin Gardner, dissections and Asian mystical symbols.

*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’m the author of several books of popular maths, including the puzzle books Can You Solve My Problems? and Puzzle Ninja.*

*In other exciting book news, you can now buy a box set of Seasons 1 to 3 of Football School. The bestselling series for 7 to 13-year-olds, written by Ben Lyttleton and me, explains the world through football, and I reckon would make an amazing Christmas gift!*