# What is a possible ordering of the vehicles serviced?

A hatchback, a limousine, a pickup, a roadster, a sedan, and a van need service through the week - Monday through Saturday - one vehicle per day.

• At least one of the vehicles is serviced later in the week than the hatchback.
• The roadster is serviced later in the week than the van and earlier in the week than the hatchback.
• Either the pickup and the van are serviced on consecutive days, or the pickup and the sedan are serviced on consecutive days, but not both.
• The sedan is serviced earlier in the week than the pickup or earlier in the week than the limousine, but not both.

Here is what I found

- At least one of the vehicles is serviced later in the week than the hatchback.TRUE
- The roadster is serviced later in the week than the van and earlier in the week than the hatchback.TRUE
- Either the pickup and the van are serviced on consecutive days, or the pickup and the sedan are serviced on consecutive days, but not both.TRUE
- The sedan is serviced earlier in the week than the pickup or earlier in the week than the limousine, but not both.TRUE

• Could you share how you set it up? – jchaykow Nov 1 '16 at 3:07

I think there's several solutions. I have

P -> S -> V -> R -> H -> L

From the clues:

• At least one of the vehicles is serviced later in the week than the hatchback.

This just means that H cannot have the last space

• The roadster is serviced later in the week than the van and earlier in the week than the hatchback.

This means that H, R, and V must be placed in the order V -> R -> H (with maybe something in between each). Also, from this and the above it follows that neither H, R or V can take the last space. Neither R or V can take the second to last, and V cannot take the third to last.

• Either the pickup and the van are serviced on consecutive days, or the pickup and the sedan are serviced on consecutive days, but not both.

This means taht P must be besides S or V, but not both. That is, the sequences V -> P -> S and V -> P -> S cannot exist, but P -> S -> V and V -> S -> P are fine.

• The sedan is serviced earlier in the week than the pickup or earlier in the week than the limousine, but not both.

This means that we need either P -> S -> L or L -> S -> P (with something in between)

My solution is jsut the first think I tried that fulfilled the above.

Multiple Solutions:

V->P->R->H->S->L
V->L->R->H->S->P
L->V->R->H->S->P
S->P->V->R->H->L
V->R->P->S->H->L

First start with a grid, days by cars, then cut out little pieces of paper, one each for each car, and move them around.