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A code consists of either a single letter or a pair distinct

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bibha
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A code consists of either a single letter or a pair distinct [#permalink] New post   08 May 2010, 09:53
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A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

A. 4
B. 5
C. 5
D. 6
E. 7
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   08 May 2010, 11:53
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bibha wrote:
1. A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

Waiting for solution
thanks :-)




Lets take it this way, if we take 4 letters A,B,C,D

then we can 4 single letter code ,

and 6 double letter code( AB, AC, AD, BC,BD, CD)

hence minimum number of letters required is 5
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   08 May 2010, 15:04
bibha wrote:
1. A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

Waiting for solution
thanks :-)


We need 5 alphabets.. A, B, C ,D ,E
Actually 5 alphabets are enough for 14 participants..but if we take only 4 alphabets we can only cover only 9 participants..!!

a, b, c, d, e
ab, ac, ad, ae
bc, bd, be,
cd, ce
de
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   08 May 2010, 15:07
nverma wrote:
bibha wrote:
1. A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

Waiting for solution
thanks :-)


We need 5 alphabets.. A, B, C ,D ,E
Actually 5 alphabets are enough for 14 participants..but if we take only 4 alphabets we can only cover only 9 participants..!!


a, b, c, d, e
ab, ac, ad, ae
bc, bd, be,
cd, ce
de
[/quote]

A small correction .. shouldn't it be 10 instead of 9 ? :D
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   08 May 2010, 15:23
nitishmahajan wrote:
nverma wrote:
bibha wrote:
1. A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

Waiting for solution
thanks :-)


We need 5 alphabets.. A, B, C ,D ,E
Actually 5 alphabets are enough for 14 participants..but if we take only 4 alphabets we can only cover only 9 participants..!!


a, b, c, d, e
ab, ac, ad, ae
bc, bd, be,
cd, ce
de


A small correction .. shouldn't it be 10 instead of 9 ? :D[/quote]

Yups buddy..Thanx
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   08 May 2010, 19:22
nverma wrote:
]


A small correction .. shouldn't it be 10 instead of 9 ? :D[/quote]

Yups buddy..Thanx[/quote]

Anytime ..!

Cheers
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   09 May 2010, 01:51
IMO 5

Total codes with 2 digit out of 5 = 5C2 = 10
and 5 digit themselves
So total 15 codes can be generated from 5 alphabets (sufficient for 12 members)
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   09 May 2010, 04:20
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bibha wrote:
1. A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

Waiting for solution
thanks :-)


Algebraic approach:

\(C^2_n+n\geq{12}\) --> \(\frac{n(n-1)}{2}+n\geq{12}\) --> \(n(n-1)+2n\geq{24}\) --> \(n(n+1)\geq{24}\) --> \(n=5\).
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   27 Dec 2015, 00:19
[quote="Bunuel"][quote="bibha"]1. A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

question mentions A code consists of either a single letter or a pair distinct letters in alphabetical order.

doesn't it indicates to use Permutations here.

Please clarify.
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   27 Dec 2015, 05:13
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smartguy595 wrote:
Bunuel wrote:
bibha wrote:
1. A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

question mentions A code consists of either a single letter or a pair distinct letters in alphabetical order.

doesn't it indicates to use Permutations here.

Please clarify.


hi,
yes the Q like this would involve Permutations....
but due to the words in alphabetical order, permutations changes to combinations..
because only one arrangement out of all possible set from a certain number of letters will be in alphabetical order...
for example.. a,b,c..
now permutation would mean abc,acb,bac,bca,cab,cba.. 6 ways but combination would be one abc or bac etc..
but due to the condition of in alphabetical order, only abc will be true..
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   07 Aug 2020, 11:52
We would require five letters. Solution is below or each case. We can make 15 cases from here.
A, B, C ,D, E
AB, AC, AD, AE
BC, BD, BE
CD, CE
DE
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   08 Aug 2020, 01:51
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Single letter or a pair of distinct letters in alphabetical order

Single letter: A, B,C, D, E

Pair: AB, AC, AD, AE
BC, BD, BE
CD, CE
DE

Total 15. Hence we need 5 letters at least.

Answer: 5
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Re: A code consists of either a single letter or a pair distinct [#permalink] New post   10 Aug 2020, 04:42
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bibha wrote:
A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?


Solution:


First, let’s guess that we use 4 letters. A single-letter code would generate 4 options: A B C D, and a double-letter code (with letters in alphabetical order) would generate 6 additional codes: AB, AC, AD, BC, BD, and CD. The total number of codes is 10, which is not sufficient for the 12 participants.

We can see, without additional work, that 5 letters will suffice for the desired number of codes. For completeness’ sake, they are listed here: A, B, C, D, E, AB, AC, AD, AE, BC, BD, BE, CD, CE, DE, and we see that the use of 5 letters generates 15 codes, which is more than sufficient.


Answer: 5
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Re: A code consists of either a single letter or a pair distinct [#permalink]
10 Aug 2020, 04:42
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