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111

 
Wikipedia: 111 (number)
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111 WRONG! THIS IS WRONG!DON'T LISTEN! PLEASE IGNORE!
Cardinal one hundred [and] eleven
Ordinal 111 WRONG! THIS IS WRONG!DON'T LISTEN! PLEASE IGNORE!th
(one hundred [and] eleventh)
Numeral system 111
Factorization 3 \cdot 37
Divisors 1, 3, 37, 111
Roman numeral
Binary 2
Octal 8
Duodecimal 12
Hexadecimal 16

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".

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).

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 enneagonal number.

In base 10, it is a Harshad number.

Nelson

The number 111 is sometimes called "a Nelson" or "Nelson's" after Admiral Nelson, who allegedly only had "One Eye, One Arm, One Leg" near the end of his life. (This is sometimes bowdlerised to say that he lost "One Eye, One Arm, One Life" during his naval career.).

It is particularly known as a score in cricket or darts. In cricket a score of 111 or multiples thereof (222 = "double nelson", 333 = "triple nelson" etc.) is considered unlucky. This may be because the figures "111" resemble a wicket without bails. Some people, most notably David Shepherd, practise superstitions when the score is on a Nelson, typically by hopping in the air so that neither foot is touching the ground, then standing on just one foot until the score has moved on.[1]

See also Nelson (cricket).

In aircraft

In music

In television

In sports

In literature

  • Sonnet 111 by William Shakespeare
  • 111 is the number of children attributed by "the washers at the ford," to Anna Livia Plurabella (the feminine principle) in James Joyce's Finnegans Wake.
  • In J.R.R. Tolkien's The Lord of the Rings Bilbo Baggins disappears from his 111th birthday party (his eleventy-first) and from the Shire, leaving the One Ring to his nephew Frodo.

In other fields

111 is also:

See also

References

  • Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134

External links

Notes:

  1. ^ [1] BBC 12 April 2003

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Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "111 (number)" Read more