111 (number)


111 (number)
111
Cardinal one hundred [and] eleven
Ordinal 111th
(one hundred [and] eleventh)
Numeral system 111
Factorization 3 \cdot 37
Divisors 1, 3, 37, 111
Roman numeral CXI
Binary 11011112
Octal 1578
Duodecimal 9312
Hexadecimal 6F16

111 (One hundred [and] eleven) is the natural number following 110 and preceding 112. It is the lowest positive integer requiring six syllables to name in American English, or seven syllables (including "and") in Canadian and British English. Occasionally it is referred to as "eleventy-one", particularly by hobbits.[1]

Contents

In mathematics

111 is a perfect totient number.

111 is R3 or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 × 37, therefore all triplets (numbers like 222 or 777) in base ten are of the form 3n × 37.

All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime. 111 is not prime in base ten, but is prime in base two, where 1112 = 710. It is also prime in these other bases up to 100: 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, and 99. 111 is also prime in base 111 (= 1243310).

In radix 18 the number 111 is the third power of seven 73 (= 34310) which is the only radix where 111 is a power.

The smallest magic square using only 1 and prime numbers has a magic constant of 111:

31 73 7
13 37 61
67 1 43

A six-by-six magic square using the numbers 1 through 36 also has a magic constant of 111:

24 16 33 23 10 5
11 15 28 8 13 36
20 14 2 31 25 19
1 18 6 29 27 30
21 22 7 17 32 12
34 26 35 3 4 9

(The square has this magic constant because 1 + 2 + 3 + ... + 34 + 35 + 36 = 666, and 666 / 6 = 111).

111 is also the magic constant of the n-Queens Problem for n = 6. It is also an nonagonal number.

In base 10, it is a Harshad number.

Nelson

The number 111 is sometimes called "a Nelson" after Admiral Nelson, who allegedly only had "One Eye, One Arm, One Leg" near the end of his life. (Which is in fact incorrect - Nelson never lost a leg.)

It is particularly known as a score in cricket. A score of 111 or multiples thereof (222 = "double nelson", 333 = "triple nelson" and so on) is considered unlucky by some in English cricket: most famously by the international umpire David Shepherd, who had a whole retinue of peculiar mannerisms - hops, shuffles, jiggles and so on - that he would indulge in if the score was ever a "Nelson" multiple. Particularly if the number of wickets also matched - 111/1, 222/2 etc.

In other fields

111 is also:

See also

References

  1. ^ John Ronald Reuel Tolkien (1993). The fellowship of the ring: being the first part of The lord of the rings. HarperCollins. ISBN 978-0-261-10235-4. http://books.google.com/books?id=VUi4RAAACAAJ. Retrieved 29 August 2011. 

External links


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