Analytical reasoning in the Guess Your Card game

Guess Your Card

Description

The "Guess Your Card" game consists of a number of players drawing from a pile of an indeterminate number of cards. Each of the cards has a number from 1 to 9 on them. The players then place their cards outward-facing on their heads, which permits other players to see the cards, but does not allow the player to see his or her own cards. The object of the game is for a player to guess which cards he or she has. During play, each player, in turn, draws a question from a stack of questions, and the player must answer the question asked based on the cards that they can see (all cards but their own).

Step One: Determine all Known Information

In the first step, the player needs to identify all information that is known. As the fourth player, the information that I know is that Andy has 1, 3 & 7; Belle has 3, 4, & 7, and Carol has 4, 6, & 8; and I have ____, ____, and ____. This is my starting point for all information.

Step Two: Include Additional Information from Clues

Next, I build upon additional information to strengthen what I know about my cards. Andy is asked, "Do you see two or more players whose cards sum to the same value?" And answers yes to the question. Andy cannot see his own cards, but see people whose cards sum to the same value. Belle's card's total to 14 and Carol's cards total to 18. Those sums are not the same. Therefore, I know that my three cards will total to either 14 or 18. In other words:

____ + ____ + ____ = 14 or 18.

Next Belle draws a question card and is asked, "Of the five odd numbers, how many different odd numbers to you see?" She answers, all of them. Belle cannot see her cards, but can see Andy and Carol's cards. Carol does not have any odd cards, but Andy has 1, 3, and 7. This means that I must have 5 and 9, since Belle can see all of the cards. I know that my set is now: 5, 9, and

Step Three: Combine all Known Information to Reach the Conclusion

Finally, I combine the different information that I know. I know that my set includes a 5 and a 9 and that my set totals to either 14 or 18. Because 5 +9 = 14, I know that my set cannot total to 14, because it must include a third card. As a result, I know that my total is 18. Therefore, I combine my knowledge to get the following logical equation:

5 + 9+ ____ = 18. As a result, I can determine that my final card is a 4.

Answer

My three cards are 4, 5, and 9.