#6 Factor factory
Set by Daniel Griller
The factors of 12 are 1, 2, 3, 4, 6 and 12. It has four even factors and two odd factors, so two-thirds of its factors are even.
What fraction of the factors of 8 are even?
How many whole numbers between 1 and 100 have the property that exactly half of their factors are even?
How many whole numbers between 1 and 1 million have the property that exactly one-third of their factors are divisible by 3?
Solution next week
#5 Diagonal lines
Solution
Generally, for a shape with n vertices, there will be n(n-3)/2 diagonals. This is because each vertex can join to n-3 others (not including those adjacent to it and itself) and there are n vertices to connect. To avoid counting each line twice, we divide by 2. Hence, a pentagon has five diagonals, a hexagon nine, while a nonagon (nine-sided shape) is the polygon that has three times as many diagonals as vertices.
Quick quiz #238
set by Bethan Ackerley
1 Which of the following UK villages is the namesake of a geological age: Kimmeridge, Tolpuddle or Studland?
2 The Vera C. Rubin Observatory was previously known by what name?
3 Which mathematician devised the cellular automaton known as the Game of Life, a type of computational model?
4 The use of penetrating waves, such as X-rays or ultrasound, to create a 3D view of the inside of the body from 2D "slices" is known as what?
5 What did the DONUT experiment detect in the late 1990s?
Quick quiz #238
Answers
1 Kimmeridge
2 The Large Synoptic Survey Telescope
3 John Conway
4 Tomography
5 The tau neutrino