04/14/03 Challenge Problem

[rchen1987]

Shouldn't the answer be C because the option for the second line:

"OR The line might look like this: (Back) Chandra X X Ken (Front)"

makes the problem statement contradictory?

"1) There are three people in front of Chandra and three people behind Ken
2) Two people are standing between Chandra and Ken"

[JonathanSchneider]

Actually, no. This is a tricky problem, and one that is probably best solved visually, by drawing out some slots and then thinking about what MUST be true versus what COULD CHANGE.

Using both statements together, we know that there are 3 people ahead of C, there are 3 people behind K, and 2 people in between them.

Think of the first part as:

_ _ _ C

Think of the second part as:

K _ _ _

And think of the third part as:

C _ _ K

or

K _ _ C

Now, given that, you can see that we have two options:

_ _ _ C _ _ K _ _ _

or

K _ _ C

Notice that in both cases all three constraints are satisfied. All we have done is move the _ _ _ C and K _ _ _ segments to show the various options. Thus, the line could be either 4 or 10 people long.