# Will You Take Coffee or Tea?

Claire, Katia and Lila like to have dinner together.

1. Each of them always orders either coffee or tea after dinner.

2. If Claire orders coffee, then Katia orders the drink that Lila orders.

3. If Katia orders coffee, then Claire orders the drink that Lila doesn't order.

4. If Lila orders tea, then Claire orders the drink that Katia orders.

According to these constraints, which of them must always order the same drink?

A simpler proof of the solution already given by the other two answers:

Let's assume Claire orders coffee. By condition 1, Katia and Lila both order the same thing, either coffee or tea.

• If it's coffee, then they're all drinking the same thing, contradicting condition 2.

• If it's tea, then Claire is drinking something different from the others, contradicting condition 3.

Either way we have a contradiction, so

Claire is always ordering tea.

• I don't get it... can't we just as easily say Lila always orders coffee and also satisfy all the conditions? Dec 8, 2020 at 17:04
• @musefan Yes exactly, Lila ordering coffee or Lila ordering tea are both possible. Here I've found a combination which is not possible, which answers the question. Dec 8, 2020 at 17:11
• I get what you are saying, and it's clearly what the OP intended. However, I could say all 3 order the same drink every time: Claire = tea, Katia = tea, Lila = coffee and there is no information in the question that contradicts that being a correct answer. Surely the question should only have one valid answer? Dec 9, 2020 at 9:45
• @musefan I think you're not getting exactly what the puzzle is. Yes, there is no unique answer to "what are all of these three people drinking" but there is a unique answer to "under the given constraints, which of these three people must always order the same drink", which is the puzzle to be solved here. In fact, the question suggests that they often have dinner together, so maybe the exact configuration of drinks varies from time to time, but one person is always ordering the same thing every time - the question asks which one of them that is. Dec 9, 2020 at 9:50
• But I just gave you an answer that fits "under the given constraints...". "Often" doesn't imply that any of them change their drink choice. It also isn't specific that only one person orders the same drink. Which I feel is the part that I have a problem with. I don't think a question should require assumptions outside of the information provided. I believe it should have a specific rule that states only one person ever orders the same drink, that way it can only have the one valid answer as you have provided. Dec 9, 2020 at 9:57

Claire does - always tea.

Because:

The possible orders, and which rule prevents it:

C | K | L
---------
T | T | T
T | T | C
T | C | T (3 & 4)
T | C | C
C | T | T (4)
C | T | C (2)
C | C | T (2)
C | C | C (3)

Of the remaining options, Claire always has tea.

• You got it ! Good job. Dec 8, 2020 at 12:43
• TCT also violates #3 as well as #4 Dec 8, 2020 at 21:25
• Ah yes, I transcribed quickly after just crossing them off on paper without tracking rules - I'll update
– lxop
Dec 8, 2020 at 21:46

Another way of looking at the problem:

Rule 1 means that

we can suppose Claire, Katia and Lila are Boolean variables! Let coffee be true, and tea be false.

So we can write the other rules as

(2) If C, then K = L

(3) If K, then C != L

(4) If !L, then C = K

Suppose C. Then K leads to a contradiction by (3), and !K leads to a contradiction by (4). Therefore !C, and Claire always orders tea.

• Nice. I would change tea be true and coffee be false, though =D Dec 8, 2020 at 8:15
• Nice work, sleuth ! You got it. Dec 8, 2020 at 12:44