If L works on the same workpiece both on Tuesday and on Thursday, which one of the following must be true about that ...

Victoria on June 5, 2020

Hi @nikkim,

This is definitely a complicated game.

One key point that I think you may have missed is that each employee must work on a piece on each given day. Therefore, the diagram should look like this:

1: _ _ _ _
2: _ _ _ _
3: _ _ _ _
4: _ _ _ _
M T W R

Now let's go through the rules.

(1) J cannot pass to M. Therefore, J can only pass to K or L.
(2) K cannot pass to J. Therefore, K can only pass to M or L.
(3) L cannot pass to J. Therefore, L can only pass to M or K.

It's also helpful to determine who each person can receive work from.

J can only receive work from M due to R2 and R3.
K can receive work from anyone.
L can receive work from anyone.
M can receive work from K or L due to R1.

Let's go back to the diagram and input that L must work on the same workpiece on both Tuesday and Thursday.

1: _ L _ L
2: _ _ _ _
3: _ _ _ _
4: _ _ _ _
M T W R

We can eliminate answer choices (A) through (C) right off the bat. We know that L can receive work from anyone. Therefore, it doesn't matter who works on Monday.

Answer choice (D) is eliminated because J can only receive work from M.

Therefore, answer choice (E) is correct.

Going back to your original question, let's input that configuration into our diagram.

1: J L M L
2: _ _ _ _
3: _ _ _ _
4: _ _ _ _
M T W R

There are so many possibilities for the next three workpieces, but they all become frustrated at some point down the line. I'll outline a couple examples to demonstrate this.

Let's start by having K work on W2 on M.

1: J L M L
2: K M J K
3: M J L M
4: L K K J

In this example, everything works out until W4 as K cannot pass to themselves nor can K pass to J. What if we start W2 with M?

1: J L M L
2: M J L K

This example becomes frustrated on W3. The only possible piece that L could work on on M is W3. We cannot have M work on it on T because J would have to either pass to K or L on R, both of whom are already assigned to pieces on that day.

We can't have M work on it on W because M is already working on W1 that day.

What if we start W2 with L?

1: J L M L
2: L M J K
3: M J K M
4: K K

This example becomes frustrated again on W4 as K cannot pass to themselves.

There are numerous other ways we could have outlined it, but all scenarios end similarly. Therefore, if L works on the same workpiece on both T and R, it MUST be true that K works on that workpiece on W. M cannot work on it on W based on the examples I've outlined above and J cannot work on it on W as J can only receive work from M.

Hope this makes sense! Try not to get too hung up on any one game and focus instead on the patterns between games. Please let us know if you have any further questions.

nikkim on June 6, 2020

Thank you for the explanation!