Final answer:
The card number that Sam selected is likely 1, as it's the only number consistent with the statements by Adriel and Kris, who each possess partial information about the card's identity.
Step-by-step explanation:
To answer the question, we need to use logical deduction based on the statements given by Adriel and Kris. Here are the important points to consider:
- Adriel knows the color of the card, and Kris knows the number on the card.
- Adriel is certain that Kris will also not be able to identify the card. This implies that the number on the card must be shared by more than one color since, otherwise, knowing the number would enable Kris to know the card if it were unique.
- Kris, after hearing that Adriel also doesn't know the card, concludes which card it is. This suggests that the number Kris knows cannot be 11 because there are 11s in three different colors, and Kris would not be able to distinguish between them just from Adriel's statement.
- The combination of Adriel's and Kris's statements leads Adriel to know the card as well. So the number must be unique among the remaining possibilities.
With these deductions, let's look at the non-11 numbers. Several numbers appear in only one color, but those could be immediately identified by Kris. So, those are not our numbers. The numbers that appear more than once and isn't 11 are 1, 5, and 12. However, 5 and 12 are present on two different colors. If either of these were chosen, Adriel would not be able to deduce the card after Kris's statement since there would be two possibilities for each number. Therefore, the only number that fits all criteria is 1 since it's the only one where its repetition is not a problem for Adriel's final deduction (as one color was already disclosed to him by Sam).
Thus, the number on the card that Sam selected must be 1.