Researcher's Code

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showoff16884: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Fri Aug 31, 2007 10:03 am; Thanked: 2 times

Researcher's Code

by showoff16884 » Mon Nov 12, 2007 4:39 pm

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. 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. 6
D. 7
E. 8

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Source: Beat The GMAT — Problem Solving | Mon Nov 12, 2007 4:39 pm

gmatguy16: Master | Next Rank: 500 Posts; Posts: 124; Joined: Thu Aug 23, 2007 5:11 am; Thanked: 2 times

by gmatguy16 » Mon Nov 12, 2007 6:01 pm

imo b
codes are as follows,try adding one at a time to find minimum necessary
1 a
2 b
3 ab
4 c
5 ac
6 bc
7 d
8 ad
9 bd
10 cd
11
12
hence using a,b,c,d 4 letters we can create 10 distinct codes,so 5 minimum are necessary.

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camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 am; Location: India; Thanked: 34 times; Followed by:5 members

by camitava » Mon Nov 12, 2007 8:59 pm

gmatguy16, the approach u followed is really appreaciatable but I took a different approach -
Now if there are n tokens, taking 2 at a time to indicate a different unique combination - the combination will be = (n - 1)!. Are you getting me, showoff16884? For more manual clarification, just refer gmatguy16's approach to take 2 tokens at a time.
Now if n = 4, (4 -1)! = 6
So total representation = two digit representation + single digit representation = 6 + 4 = 10 -> NOT SUFF for 12 people.
So the least no of alphabets to chose is = 5. Am I clear to explain?

Correct me If I am wrong

Regards,

Amitava