**0** is the additive identity.

**1** is the multiplicative identity.

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** 2** is the only even prime.

**3** is the number of spatial dimensions we live in.

**4** is the smallest number of colors sufficient to color all planar maps.

**5** is the number of Platonic solids.

**6** is the smallest perfect number.

**7** is the smallest number of integer-sided rectangles that tile a rectangle so that no 2 rectangles share a common length.

**8** is the largest cube in the Fibonacci sequence.

**9** is the maximum number of cubes that are needed to sum to any positive integer.

**10** is the base of our number system.

**11** is the largest known multiplicative persistence.

**12** is the smallest abundant number.

**13** is the number of Archimedian solids.

**14** is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.

**15** is the smallest composite number n with the property that there is only one group of order n.

**16** is the only number of the form xy = yx with x and y different integers.

**17** is the number of wallpaper groups.

**18** is the only number that is twice the sum of its digits.

**19** is the maximum number of 4^{th} powers needed to sum to any number.

**20** is the number of rooted trees with 6 vertices.

**21** is the smallest number of distinct squares needed to tile a squares.

**22** is the number of partitions of 8.

**23** is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.

**24** is the largest number divisible by all numbers less than its square root.

**25** is the smallest square that can be written as a sum of 2 squares.

**26** is the only number to be directly between a square and a cube.

**27** is the largest number that is the sum of the digits of its cube.

**28** is the 2^{nd} perfect number.

**29** is the 7^{th} Lucas number.

**30** is the largest number with the property that all smaller numbers relatively prime to it are prime.

**31** is a Mersenne prime.

**32** is the smallest 5^{th} power (besides 1).

**33** is the largest number that is not a sum of distinct triangular numbers.

**34** is the smallest number with the property that it and its neighbors have the same number of divisors.

**35** is the number of hexominoes.

**36** is the smallest number (besides 1) which is both square and triangular.

**37** is the maximum number of 5^{th} powers needed to sum to any number.

**38** is the last Roman numeral when written lexicographically.

**39** is the smallest number which has 3 different partitions into 3 parts with the same product.

**40** is the only number whose letters are in alphabetical order.

**41** is the smallest number that is not of the form │2x – 3y│

**42** is the 5^{th} Catalan number.

**43** is the number of sided 7-iamonds.

**44** is the number od derangements of 5 items.

**45** is a Kaprekar number.

**46** is the number of differentarrangements (up to rotation and reflection) of 9 non-attacking queens on a 9x9 chessboard.

**47** is the largest number of cubes that cannot tile a cube.

**48** is the smallest number with 10 divisors.

**49** is the smallest number with the property that it and its neighbors are squareful.

**50** is the smallest number that can be written as the sum of 2 squares in 2 ways.