Brain Teasers
Cornerstones !!!
Six boys A, B, C, D, E and F have to stand in a row. B and C are together, but they cannot be at either of the ends. F is at the right of E and there is exactly one boy between them. D cannot be next to F. Who should always stand at one of the ends?
Answer
D must always stand at one of the ends.The observations that can be derived are:-
1) B and C are together, but they cannot be at either of the ends.
2) F is at the right of E and there is exactly one boy between them.
3) D cannot be next to F.
Let us first number the positions from 1 to 6(from left to right), place E and F in different positions and analyze the cases.
From observation 2, we can derive the following cases:-
Case 1 2 3 4 5 6
1 _ _ _ E _ F
2 _ _ E _ F _
3 _ E _ F _ _
4 E _ F _ _ _
where the blank spaces indicate positions where the others stand.
Considering each of the above cases individually we have,
Case 1 : B, C and D cannot go into position 5, since B and C are together always and D cannot be next to F from observations 1 and 3 respectively. Hence A must go into position 5 and D into position 1 (since from observation 1, B and C cannot be at either of the ends).
Case 2 : B and C cannot be given positions 1 and 2 (since from observation 1, B and C cannot be at either of the ends), neither do they fit into any other positions in this case. Hence this case is not possible.
Case 3 : B and C cannot be given positions 5 and 6 (since from observation 1, B and C cannot be at either of the ends), neither do they fit into any other positions in this case. Hence this case is also not possible.
Case 4 : B, C and D cannot go into position 2, since B and C are together always and D cannot be next to F from observations 1 and 3 respectively. Hence A must go into position 2 and D into position 6 (since from observation 1, B and C cannot be at either of the ends).
From the above 4 cases it is clear that one of the cornerstones must always be D and the other can be either of E or F.
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Comments
Now I know my ABCs good teaser
Well, I'm still a beginner, but I got that one pretty quick. I didn't have to go through all that figuring either. It was good, though. Even if it doesn't take long, it still takes some figuring.
nice!
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