Can you solve it? Cutting the perfect slice

Author
Alex Bellos
Event type
Description

Fuente: The Guardian-22 Octubre 2018

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.

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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?

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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.

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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].

UPDATE: to read the solutions click here.