Building cars

[BMAD]

You are in charge of building cars, you are tasked to build exactly one car a day (no more, no less) and to be clear a partial car is as good as not building a car.  Your shift is separated into two parts in which you could either build a whole, half, third, fourth, or fifth of a car in a given shift.  By the end of the week you are to have built 7 cars with no partial cars left over.  How many ways can this be done assuming a 7-day work week?

Edited January 22, 2018 by BMAD

[bonanova]

I'm not understanding something about two shifts building exactly one car.
A whole car (in one shift) or two half-cars (in two shifts) seem to be the only cases.

Maybe spoiler one other possibility as a means of explaining?  Thanks.

[BMAD]

22 minutes ago, bonanova said:

I'm not understanding something about two shifts building exactly one car.
A whole car (in one shift) or two half-cars (in two shifts) seem to be the only cases.

Maybe spoiler one other possibility as a means of explaining?  Thanks.

The only day where you cannot have a partial car built is the 7th day.  The other days must have a whole car built to meet your quota but you can have part of a car as long as you don't make two in a given day.  You must build something each shift.

[bonanova]

So when OP says

"build exactly one car a day (no more, no less)"

it means you can build any number of cars in the interval [1 2) because

"and to be clear a partial car is as good as not building a car."

So if you built 1 1/3 cars on the first day it would count as "exactly 1 car," because it would pass 1/3 of a car to the second day, when you would then have to build any number of cars in the interval [2/3, 1 2/3)?

In general, is it correct to believe that at the end of every nth day you must have built [n, n+1) cars, except for n=7, after which you must have exactly 7 cars?

[BMAD]

16 hours ago, bonanova said:

So when OP says

"build exactly one car a day (no more, no less)"

it means you can build any number of cars in the interval [1 2) because

"and to be clear a partial car is as good as not building a car."

So if you built 1 1/3 cars on the first day it would count as "exactly 1 car," because it would pass 1/3 of a car to the second day, when you would then have to build any number of cars in the interval [2/3, 1 2/3)?

In general, is it correct to believe that at the end of every nth day you must have built [n, n+1) cars, except for n=7, after which you must have exactly 7 cars?

yes, exactly.