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There are 553 members of the Warwick Mathematics Society, of which 0 are new today!
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Number game

Callan
Post Icon Posted: Submitted by Callan on 14 June 2009 - 9:56pm.

Joined: 2008-09-30
Posts: 173

You probably already know this game already but basically as inspired by the following paradox, http://en.wikipedia.org/wiki/Interesting_number_paradox , you have to name an interesting property of each natural number in the usual ordering ;). Someone can start with 0 or 1.

‹ Achievement Unlocked: Posted new forum topic band practice ›
cosmin
Post Icon Posted: 14 June 2009 - 11:02pm

Joined: 2006-11-02
Posts: 1291

0: The number of words in the English language containing the string "EWQ".
dsmccormick
Post Icon Posted: 14 June 2009 - 11:18pm

Joined: 2006-10-06
Posts: 75

1: The number of weeks it takes to travel from Moscow to Vladivostok by train.
cosmin
Post Icon Posted: 15 June 2009 - 2:14am

Joined: 2006-11-02
Posts: 1291

2: The only prime $ p $ for which the ring $ \{x + iy + ju + kv : x,y,u,v \in \mathbb{Q}_p\} $ (with normal quaternion multiplication and addition) is an integral domain.
owen.daniel
Post Icon Posted: 15 June 2009 - 8:03am

Joined: 2007-10-07
Posts: 93

3: The number of Aristotle's unities. The Unity of Time, Place, and Action which describe the foundations of Greek tragedy.
Sam
Post Icon Posted: 15 June 2009 - 10:30am

Joined: 2007-10-03
Posts: 562

4: The maximum number of colours required to colour a planar graph.
cosmin
Post Icon Posted: 15 June 2009 - 12:33pm

Joined: 2006-11-02
Posts: 1291

5: The maximum number of colours required to list colour a planar graph.
Callan
Post Icon Posted: 15 June 2009 - 12:38pm

Joined: 2008-09-30
Posts: 173

6: The smallest perfect number.
Sam
Post Icon Posted: 15 June 2009 - 12:40pm

Joined: 2007-10-03
Posts: 562

7: The only prime number $ p $ such that $ p-2 $ and $ p-4 $ are also prime.
cosmin
Post Icon Posted: 15 June 2009 - 1:55pm

Joined: 2006-11-02
Posts: 1291

8: The least integer $ n $ for which the group of units of $ \mathbb{Z}/n\mathbb{Z} $ is not cyclic.
cosmin
Post Icon Posted: 15 June 2009 - 1:56pm

Joined: 2006-11-02
Posts: 1291

9: The number of imaginary quadratic fields with class number 1.
ka7th
Post Icon Posted: 15 June 2009 - 3:51pm

Joined: 2007-10-08
Posts: 107

10: the smallest number with a multiplacative persistance of 1.
owen.daniel
Post Icon Posted: 15 June 2009 - 5:52pm

Joined: 2007-10-07
Posts: 93

11: The top volume attainable by Nigel Tuffnel's amp.
dsmccormick
Post Icon Posted: 16 June 2009 - 1:20am

Joined: 2006-10-06
Posts: 75

12: The order of the smallest group not to have subgroups of all sizes dividing its order (that is, $ A_4 $ has no subgroup of order 6).
Smithers
Post Icon Posted: 18 June 2009 - 6:51pm

Joined: 2006-10-18
Posts: 41

13: The maximum number of same-sized spheres (in $ \mathbb{R}^3 $) with disjoint interiors such that one is tangent to all of the others.
cosmin
Post Icon Posted: 20 June 2009 - 12:58am

Joined: 2006-11-02
Posts: 1291

14: The largest number of subsets that can be obtained by repeatedly applying the operations of closure and complement to a given subset of a topological space.
Callan
Post Icon Posted: 22 June 2009 - 12:16am

Joined: 2008-09-30
Posts: 173

15: The usual number of tiles in the n-puzzle (where legal moves in fact generate $ A_{15} $ using a certain correspondence).
Sam
Post Icon Posted: 22 June 2009 - 2:00pm

Joined: 2007-10-03
Posts: 562

16: The only natural number that can be written as $ n = a^b = b^a $ for distinct natural numbers $ a $ and $ b $.
Callan
Post Icon Posted: 22 June 2009 - 2:02pm

Joined: 2008-09-30
Posts: 173

17: The number of distinct wallpaper tiling groups (up to affine transformations).
Sleeping Yeti
Post Icon Posted: 25 June 2009 - 11:53am

Joined: 2007-03-03
Posts: 196

18: The smallest number that can be represented as a sum of 3 distinct primes in 2 different ways:

18 = 2+3+13
18 = 2+5+11
Sam
Post Icon Posted: 4 July 2009 - 1:45am

Joined: 2007-10-03
Posts: 562

19: The smallest $ n $ such that every natural number is the sum of $ n $ fourth powers of natural numbers.
cosmin
Post Icon Posted: 4 July 2009 - 10:32am

Joined: 2006-11-02
Posts: 1291

20: The largest possible number of faces in a Platonic solid.
ka7th
Post Icon Posted: 5 July 2009 - 2:49pm

Joined: 2007-10-08
Posts: 107

21: the smallest number that can be expressed as the sume of at most 3 triangle numbers in 4 different ways.
ka7th
Post Icon Posted: 7 July 2009 - 8:57pm

Joined: 2007-10-08
Posts: 107

22: The smallest non-trivial number (thats is >1) such that the number of digits in n!=n that is 22! has 22 digits.
Sam
Post Icon Posted: 7 July 2009 - 9:01pm

Joined: 2007-10-03
Posts: 562

23: The number of problems in Hilbert's list of unsolved problems that he presented at the 1900 International Congress of Mathematicians in Paris.
cosmin
Post Icon Posted: 10 July 2009 - 1:34pm

Joined: 2006-11-02
Posts: 1291

24: All Dirichlet characters mod $ n $ are real if and only if $ n\mid 24 $.
ka7th
Post Icon Posted: 11 July 2009 - 6:44pm

Joined: 2007-10-08
Posts: 107

25: The only square 2 less than a cube (25=27-2, 27=33, 25=52).
cosmin
Post Icon Posted: 19 July 2009 - 12:36am

Joined: 2006-11-02
Posts: 1291

26: The number of sporadic groups. (courtesy of Callan)
Callan
Post Icon Posted: 21 July 2009 - 12:49am

Joined: 2008-09-30
Posts: 173

27: The number of straight lines on any smooth cubic surface.
Callan
Post Icon Posted: 21 July 2009 - 12:51am

Joined: 2008-09-30
Posts: 173

28: The number of differentiable structures on $ S^{7} $ (up to diffeomorphism).
ka7th
Post Icon Posted: 23 July 2009 - 9:33am

Joined: 2007-10-08
Posts: 107

29: the third smallest number (after 1 and 5) and second smallest prime such that 2.n2-1 is a square (n=29, 2.292-1=1681=412)
dsmccormick
Post Icon Posted: 19 August 2009 - 7:37pm

Joined: 2006-10-06
Posts: 75

30: The smallest number with three distinct prime factors (2, 3 and 5).
Callan
Post Icon Posted: 17 September 2009 - 3:37pm

Joined: 2008-09-30
Posts: 173

31: Turkish slang for masturbation.
Sleeping Yeti
Post Icon Posted: 23 October 2009 - 9:35am

Joined: 2007-03-03
Posts: 196

32: the first number such that no month of our calendar has that many days.
cosmin
Post Icon Posted: 24 October 2009 - 12:26am

Joined: 2006-11-02
Posts: 1291

33: The largest integer that cannot be expressed as a sum of three triangular numbers.
Callan
Post Icon Posted: 25 October 2009 - 11:33pm

Joined: 2008-09-30
Posts: 173

34: Rule 34 of the internet states "If it exists, there is porn of it. No exceptions"
Smithers
Post Icon Posted: 27 October 2009 - 4:05pm

Joined: 2006-10-18
Posts: 41

35: Rule 35 - "If it doesn't, then you must create it."
cosmin
Post Icon Posted: 28 October 2009 - 11:24am

Joined: 2006-11-02
Posts: 1291

36: The largest square size for which orthogonal latin squares do not exist (Euler's 36 officers problem).
ka7th
Post Icon Posted: 29 October 2009 - 7:08pm

Joined: 2007-10-08
Posts: 107

37: the smallest (non-trivial) prime whose individual digits are also primes and suching the unit digit is a prime.
Sleeping Yeti
Post Icon Posted: 5 November 2009 - 12:07am

Joined: 2007-03-03
Posts: 196

38: Homer Simpson's age.
Sleeping Yeti
Post Icon Posted: 5 November 2009 - 12:09am

Joined: 2007-03-03
Posts: 196

39: the age that many people seem to remain at for several years on end, ladies especially (aren't misogyny Wednesdays grand?).
ka7th
Post Icon Posted: 26 November 2009 - 1:15am

Joined: 2007-10-08
Posts: 107

40: The only number when spelt in english, ie forty, the letters come in alphabetical order.
Callan
Post Icon Posted: 17 December 2009 - 9:23pm

Joined: 2008-09-30
Posts: 173

41: $ n^2−n+41 $ is prime for $ 0<n<41 $.
Callan
Post Icon Posted: 17 December 2009 - 9:25pm

Joined: 2008-09-30
Posts: 173

42: The answer to the ultimate question of life, the universe, and everything.
Sam
Post Icon Posted: 18 December 2009 - 1:03am

Joined: 2007-10-03
Posts: 562

43: The smallest atomic number for which no atom with that atomic number has any stable isotopes.
thrillz
Post Icon Posted: 5 January 2010 - 11:27pm

Joined: 2007-11-04
Posts: 16

44: The number of fucks there would actually be in this fucked up rhyme if he said fuck two more times.
Sleeping Yeti
Post Icon Posted: 2 February 2010 - 5:06am

Joined: 2007-03-03
Posts: 196

45: The smallest order of finite groups such that Sylow's theorems are not sufficient to prove their non-simplicity.

[edit]: Should have said "smallest non-trivial non-simple group such that..." since, obviously, Sylow's theorems are not sufficient to prove the non-simplicity of simple groups (no theorems are).
Jonathan Elliott
Post Icon Posted: 5 February 2010 - 6:19pm

Joined: 2006-10-16
Posts: 8

46: The number of human chromosomes.
Sleeping Yeti
Post Icon Posted: 5 March 2010 - 8:24pm

Joined: 2007-03-03
Posts: 196

47: the smallest number with 9 representations as a sum of 3 distinct primes
Sleeping Yeti
Post Icon Posted: 5 March 2010 - 8:29pm

Joined: 2007-03-03
Posts: 196

48: The smallest number with precisely 10 natural divisors.

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