Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 20
- 20 is the maximum number of moves needed to solve the Rubik's cube, also called the God's number
- In a game of chess both players have 20 first moves from which to choose
- 20 is the smallest number that cannot be either prefixed or followed by one digit to form a prime
- 20 is the largest number of set cards without a set
- 20 is the smallest number n such that 6n-1 and 6n+1 are composites
Rare Properties of 20
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
A tetrahedral number is the number of balls you can put in a triangular pyramid.
This is the space generalization of triangular and square numbers.
Common Properties of 20
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
A number is even if it is divisible by 2.
Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.