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

Question

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. 3
B. 4
C. 5
D. 6
E. 7

Show Answer

Official Answer

C

A. 3
B. 4
C. 5
D. 6
E. 7

cipher · Answer

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

nverma · Answer

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

cipher · Answer

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

nverma · Answer

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

Yups buddy..Thanx

cipher · Answer

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

Yups buddy..Thanx

Anytime ..!

Cheers

hardnstrong · Answer

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)

Bunuel · Answer

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 .

sairam595 · Answer

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 :-)

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.

chetan2u · Answer

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..

AnishaC · Answer

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

MathRevolution · Answer

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

ScottTargetTestPrep · Answer

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

Adit_ · Answer

With 4 letters you can cover 10 codes if I'm not mistaken but you're right otherwise that it cant cover all 12.
Take 2 extremes, A and D.
You can find codes in 4C2 ways = 6 ways in alphabetical order (no arranging because only 1 way fits so we only choose)
and remaining single letters A,B,C,D. 
Therefore 6+4=10

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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