[問題]GWD17-02

[fsab00037748]

Q2:
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 alphabetic 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

答案是B

請教這該怎麼做？
還有either a single letter or a pair of distinct letters
是指A,AB,BA...都可以嗎?

先謝過啦^^

[simonyu]

"either a single letter or a pair of distinct letters written in alphabetic order" 是指用一個字母或二個字母按字母順序排列

假設只有二個字母，ex:A,B，則有A,B,AB三種可能
三個字母，ex:A,B,C，則有A,B,AB,C,AC,BC六種可能
四個字母，ex:A,B,C,D，則有A,B,AB,C,AC,BC,D,AD,BD,CD十種可能
五個字母，ex:A,B,C,D,E，則有A,B,AB,C,AC,BC,D,AD,BD,CD,E,AE,BE,CE,DE十五種可能

因為只有十二個參加者，所以五個字母就夠了。
另，其實字母不一定要緊臨，上面舉的例子只是要表達在字母序上的相對關係而已。

[fsab00037748]

謝謝 simonyu大 詳細的解說 ^^