Topic: What is the mystery card?
 Message: Posted by: Scott Cram (Apr 25, 2004 07:54PM)
I have a stack of 14 cards. The third card from the top is the eight of spades. The eleventh card from the top is the seven of clubs. I've stacked the cards so that if you look at any three consecutive cards, their values will always total 18.

What is the value of the seventh card from the top of the stack?
 Message: Posted by: usa (Apr 26, 2004 01:40AM)
3
 Message: Posted by: MacGyver (Apr 26, 2004 03:22AM)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
X-X-8-X-X-X-Z-X-X-X--7--X--X--X

Here are some thoughts:

Ok, This would have to be a repeating stack, right?

Because if A+B+C = 18, then you have B+C+X = 18, then X would have to equal A. So then you could rewrite it as: B+C+A = 18, and if you move another down you would have C+A+X = 18, so X could only be equal to B.

Since we know that Out of A, B, C, one is 7 and one is 8, the last would have to be 3. Since we know the position of 7 and 8, we can work out that:

1 2 3 4 5 6 7 8 9 10 11 12 13 14
3-7-8-3-7-8-3-7-8-3--7--8--3--7

So the 7th position would be what USA said, 3.

I wonder why you mention suits though, since there are Five 3's and 7's, and four 8's, which means there has to be a duplicate 3 and 7 in there somewhere.

So I Agree with usa, but thought I'd post the thought process to arrive at that.
 Message: Posted by: Scott Cram (Apr 27, 2004 10:20AM)
I just said I had a stack of 14 cards. I didn't say they were all from the same deck.
;)