Alphabet Group

Copyright 2010 by Paul Niquette. All rights reserved.


 
are the only three letters that meet all 14 conditions listed in the puzzle.
 
 [1] Letters in the English alphabet
26
 [2] Letters formed with straight lines
15
 [3] Letters formed without lifting pencil
14
 [4] Letters that take indefinite article "an"
12
 [5] Letters pronounced with an initial "eh"
6
 [6] Consonants
21
 [7] Consonants taking indefinite article "an"
8
 [8] Consonants pronounced with an initial "eh"
6
 [9] Consonants that are voiced
13
[10] Triads available for license-plates
17,576
[11] Triads with no repetitions
15,600
[12] Triads in alphabetical order
17,576
[13] Triads in consecutive alphabetical order
22
[14] Triads that are abbreviations in real life
31

[1] Letters in the English alphabet are the same as those in the modern Latin or Roman alphabet but distinguished from the Archaic Latin alphabet: ABCDEFZHIKLMNOPQRSTVX.

[2] Letters formed with straight lines are readily discovered by grammar schoolers on the playgroud: AEFHIKLMNTVWXYZ.

[3] Letters formed without lifting pencil are likely indoor discoveries: CDIJLMNOPSUVWZ.

[4] Letters that take indefinite article "an" include all the vowels, of course, AEIOU (but not Y) along with certain consonants FLMNRSX.

[5] Letters pronounced with an initial "eh" are all consonants FLMNSX, decidedly not E.

[6] Consonants are plentiful BCDFGHJKLMNPQRSTVXZ plus Y and W most of the time.

[7] Consonants taking indefinite article "an" were included in [4] above FHLMNRSX

[8] Consonants pronounced with an initial "eh" were included in [7] above FLMNSX.

[9] Consonants that are voiced are BDGJLMNRVWXYZ, some in order to distinguish them from other consonants: B|P, D|T, G|K, V|F, Z|S.

[10] Triads available for license-plates are abundant; 263 produces an exhaustive count, which combined with, say, four decimal digits means that 10,000 vehicles might wear LMN.
[11] Triads with no repetitions will be fewer (26.25.24 vs 26.26.26), but LMN makes the cut.

[12] Triads in alphabetical order having the same total as [10] may surprise some solvers.  It assumes that [a] any triad can be put in alphabetical order and [b] XXX is in alphabetical order. For triads that can be selected from the alphabet in alphabetical order the number is 2,600.

[13] Triads in consecutive alphabetical order are as follows: ABC, BCD,...LMN,...WXY, XYZ.

[14] Triads that are abbreviations in real life were identified for LMN as follows:

Laboratory for Micro and Nanotechnology, lateral mammillary nucleus, lateral mesencephalic nucleus, Leadership and Management in Nursing, Legalize Marijuana Now, Lesbian Moms Network, library management network, Licium Multimedia Newsletter, Lifetime Movie Networks, Lio Marketing Network, Liquid Magnesium Networks, Little Miss Nicap, Livestock Monitor Newsletter, Local Media Network, Local Member Network, Local Model Networks, London Metropolitan Network, longitudinal motor neurones, Louisville Music News, low molecular nucleophilic substances, Lower Merion and Narberth, Lower Motor Neurons, Loyalty Management Netherlands, lupus membranous nephropathy, lymphoid and myeloid neoplasms. 
Bonus Puzzle
Which category in the table can be used to characterize exactly 13 of the first 100 integers.
 
Category [4] Letters (or integers) that take indefinite article "an"

Here they are: an eight, an eleven, an eighteen, an eighty, an eighty-one,... and an eighty-nine.

Now, if the word 'integer' were to be replaced with 'number', the total number of numbers would become infinite.  The fraction of all numbers between 0 and 100 in such expressions as...

  • High-tech companies on NASDAQ showed an 11.25% return on sales.
  • One custom hybrid established an 80.1 MPG fuel economy record.
  • Polling gives the legislature an 8.9% approval rating for that vote.
...will nevertheless amount to exactly 13% as limited by Category [4].

 


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