A candidate for public office plans to visit each of the six cities J, K, L, M, N and O exactly once during her campaign. Her aides are setting up the candidate's schedule according to the following restrictions :
The candidate can visit M only after she has visited both L and N.
The candidate cannot visit N before J.
The second city visited by the candidate must be K.
If the candidate visit O first, which city could she visit third ?
`{:("I. J II. L III. M "),("1) I only 2) III only 3) I and II only"),("4) II and III only 5) I, II and III"):}`

Answer

3

Explanation

Begin by summarising the infrormation: `(L+N)ltM`
`JltN`
K=2
Note: Since the candidate cannot visit two simultaneously, the condition " The candidate cannot visit N before J" is equivalent to " She must visit J before N."
Begin by entering the additional information on a diagram:
`{:("1 2 3 4 5 6"),("O K "):}`
Next, we reason that J, N and L must all come before M, which means that M comes last :
`{:("1 2 3 4 5 6"),("O K M"):}`
The only condition left to take care of is that requires J before N, but still leaves three possibilities :

So, either J and L could be third.