快猫短视频

#26 Up and down

Set by Peter Rowlett

Which is bigger, 30 脳 30 or 29 脳 31?

If we choose a number other than 30 and compare its product with itself to the product of the numbers one above and one below it, which is bigger? Does this always work the same way?

If you choose any two numbers that are above and below 30 by the same amount, what is the difference between their product and 30 脳 30?

Solution next week

#25 Triangles in circles

Solution

From seven points you can make four triangles, and from 12 points, 12 triangles. There will be either one, two or three groups of unused points, with the groups separated by the triangle鈥檚 corners; each grouping gives a different triangle. For seven points, there are four unused points, which can be grouped in four ways: (4), (3,1), (2,2), (2,1,1)

For 12 points, nine are unused, which can be grouped in 12 ways: (9), (8,1), (7,2), (6,3), (5,4), (7,1,1), (6,2,1), (5,3,1), (4,4,1), (5,2,2), (4,3,2), (3,3,3).