# Working schedule (with explanation) [closed]

Alice, Bob, Chris, Dave, Eric, Fred and Laura used to work in a restaurant 6 days a week, from Tuesday to Sunday (Monday is a day off). Every one works at least for one day, and at least two people work on each day.

Considering the following restrictions:

1. Either Alice or Bob work on the first day;
2. Laura works only on the fourth and fifth day;
3. A one-day gap is left between Laura and Chris work days;
4. Eric works on the days immediately following the ones in which Bob works.

What is the working schedule of the seven employees? A good explanation of the solution to this puzzle, rather than only the right answer, is kindly welcome.

• I do not get the Introduction. 7 Staff member, 6 working days, Monday is a day off. What is the meaning of "every one is worked for one day and at least 2 members work on a day"? – Volker Weber Mar 16 '15 at 15:06
• Also, do two people work at the same time, or are there two shifts during the day? – Aggie Kidd Mar 16 '15 at 15:08
• @buffo Sorry i too don't understand that only... – user10252 Mar 16 '15 at 15:11
• There are not enough clues to get a unique solution and the description also seems not complete. – Ivo Beckers Mar 16 '15 at 15:38
• I agree, there aren't enough clues to get a unique solution: I just managed to find three different solutions in 5 minutes... You should edit the question adding additional information, or at least provide a source. – Marco Bonelli Mar 16 '15 at 15:59

So here is a solution that I can come up with for the puzzle. It is not the only solution, as you will see.

First, I will create a table with the possibilities:

        Tu   We   Th   Fr   Sa   Su
Alice
Bob
Chris
Dave
Eric
Fred
Laura


Now lets look at the clues.

1. Laura works only on the fourth and fifth day

So we can modify her row in the table to this:

        Tu   We   Th   Fr   Sa   Su
Laura   X    X    X    *    *    X

1. A one-day gap is left between Laura and Chris work days

We can determine Chris must work on a Wednesday, the only day for which there is a one day gap. Chris may work on Tuesdays as well, but the other days are eliminated.

        Tu   We   Th   Fr   Sa   Su
Chris   ?    *    X    X    X    X

1. Eric works on the days immediately following the ones in which Bob works.

We know that Eric cannot be on Tuesday, since he must work the day after Bob. Also, Bob cannot be Sunday because Erik must work after.

So here is our complete table so far:

        Tu   We   Th   Fr   Sa   Su
Alice   ?    ?    ?    ?    ?    ?
Bob     ?    ?    ?    ?    ?    X
Chris   ?    *    X    X    X    X
Dave    ?    ?    ?    ?    ?    ?
Eric    X    ?    ?    ?    ?    ?
Fred    ?    ?    ?    ?    ?    ?
Laura   X    X    X    *    *    X


This brings us to the end of the hard constraints. Now, we have freedom to fill make some choices.

1. Either Alice or Bob work on the first day

Lets say Alice works Tuesday, and that Bob does not. This also affects the days Eric can work.

        Tu   We   Th   Fr   Sa   Su
Alice   *    ?    ?    ?    ?    ?
Bob     X    ?    ?    ?    ?    X
Chris   ?    *    X    X    X    X
Dave    ?    ?    ?    ?    ?    ?
Eric    X    X    ?    ?    ?    ?
Fred    ?    ?    ?    ?    ?    ?
Laura   X    X    X    *    *    X


Now, notice not everyone is working - Bob, Dave, Eric and Fred are not working. Also, all the days need at least one more worker, some (Thursday and Sunday) need two.

Only Bob and Eric place requirements on each other, so lets fit them in the schedule first, with Bob on Thursday, and thus Eric on Friday.

        Tu   We   Th   Fr   Sa   Su
Alice   *    ?    ?    ?    ?    ?
Bob     X    X    *    X    ?    X
Chris   ?    *    X    X    X    X
Dave    ?    ?    ?    ?    ?    ?
Eric    X    X    X    *    ?    ?
Fred    ?    ?    ?    ?    ?    ?
Laura   X    X    X    *    *    X


Now, we need one more worker on each of Tuesday, Wednesday, Thursday, and Saturday. Sunday needs two workers. Everyone is working at least once except for Dave and Fred.

So lets use them to finish a minimal schedule.

        Tu   We   Th   Fr   Sa   Su
Alice   *
Bob               *
Chris        *
Dave    *         *              *
Eric                   *
Fred         *              *    *
Laura                  *    *


This is a valid schedule, but it is by no means the only one. Dave and Fred, for example, could work every day instead and the schedule would still be valid.

As it stands, this question is not well defined; there are too many possible solutions. Perhaps there are some missing constraints? Some examples could include:

• everyone must work the same number of days
• some restrictions on dave and/or eric