Three cards are drawn from a regular deck of 52 cards and are placed face-down on a table. Alyssa, Brandon, and Christina are told that
a. the numbers are all different (Ace = 1, Jack = 11, Queen = 12, King = 13)
b. the sum of the three numbers is 13, and
c. they are in increasing order, left to right
First Alyssa looks at the number on the leftmost card and says, “I don’t have enough information to determine the other two numbers.” Then Brandon looks at the number on the rightmost card and says, “I don’t have enough information to determine the other two numbers.” Finally, Christina looks at the number on the middle card and says, “I don’t have enough information to determine the other two numbers.” Assume that each person knows that the other two reason perfectly and hears their comments, what is the number on the middle card? (Due March 7, 2008)
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3 comments:
The answer has to be one of the following:
1+2+10
1+3+9
1+4+8
1+5+7
2+3+8
2+4+7
2+5+6
3+4+6
If the first person cannot tell what the other two cards are after looking at the left most card, then we can cross out the last case 3+4+6. If the left most card was a 3, then the other two cards must be 4 and 6. I don't know what to do next.
The answer can't be 1+2+10, can't be 1+3+9, and can't be 2+5+6 because if the last card is a 6, there is only one possibility. It goes for 9 and 10 too.
So the only possible cases are
1+4+8
1+5+7
2+3+8
2+4+7
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