Diagram

[ohthatpatrick]

This is a Hybrid of Ordering and Grouping.

We have 7 things, and we need to assign them to 5 days.

This initially suggests that on two days we'll have to double up.

3 of the days - have exactly one thing
2 of the days - have exactly two things
============
total - seven things

The game's rules actually specify that only 2 of the days MUST have exactly one thing (X and U are the only full day jobs). But the numbers will still work out that we have 3 singles and 2 doubles.

So,
2 of the days - have exactly one thing, X or U, nothing else
2 of the days - have exactly two things, from NOPST
and so
1 of the days - has exactly one thing, from NOPST

Remember when you see Mismatched Ordering to run through the numerical possibilities of how the # of things will work with the # of spots.

Because each day has the upper possibility of 2 things, I would want a diagram with 2 slots per day.

__ __ __ __ __
__ __ __ __ __
M. Tu. W. Th. F

For X and U, who each take up an entire day, we'll make sure we cross out the spot above them.

For example, on Wed, we'll have
/
X

And whatever day U ends up on will look like
/
U

The only other thing we have to deal with is
S - P
N

SN will take up a day, and P has to be sometime after that day.

Our final diagram might look something like this
__ __ / __ __
__ __ X __ T
M Tu W Th F
~P

O is a floater. We know we will always have U take up a day, X take up a day, and NS take up a day.

With the remaining two days (four spots), we need to place P, T, and O. Since we already know that T is on Friday, we already know that Friday is one of those remaining two days for P, T, and O.

The number one priority is figuring out the NS day, and the number two priority is figuring out the U day. Then we can figure out where P and O could/must go.