A, B and C went bird watching. Each of them saw one bird that none of the others did. Each pair saw one bird that the third did not. And one bird was seen by all three. Of the birds A saw, two were yellow. Of the birds B saw, three were yellow. Of the birds C saw, four were yellow.

(a) How many yellow birds were seen in all?
(b) How many non-yellow birds were seen in all?

A,B, AND C EACH SAW A UNIQUE BIRD. CALL THEM 1,2, AND 3. NOW THE PAIRS...AB SAW 4 BC SAW 5 AC SAW 6. ALL 3 WATCHERS SAW BIRD 7. 7 TOTAL BIRDS.

C SAW 3,5,6, AND 7, AND FROM THE CLUE THEY ALL HAD TO BE YELLOW. A SAW 4 BIRDS, 2 OF WHICH ARE YELLOW, 1,4,6, AND 7. WE KNOW 6 AND 7 WERE YELLOW, SO 1 AND 4 ARE NOT YELLOW. B SAW 4 BIRDS, 3 OF WHICH ARE YELLOW, 2,4,5, AND 7. 5 AND 7 ARE YELLOW, 4 IS NOT, SO NOW 2 HAS TO BE YELLOW.

5 YELLOW BIRDS...2,3,5,6, AND 7.

2 NON-YELLOW BIRDS...1 AND 4.

Posted by Jim on 2004-08-02 11:14:13