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?
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Submitted by Ravi Raja
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Rating: 2.3333 (6 votes)
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Solution:
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Three birds were seen by one person each, three were seen by each unique pair (A-B, A-C, and B-C), and one was seen by all three. So seven birds were seen in all, and each person saw a total of four. Hence, all of the birds C saw were yellow. These four birds are: (1) the one C saw alone, (2) the one C saw with A, (3) the one C saw with B, and (4) the one all three saw together. This accounts for both of the yellow birds A saw, and two of the three yellow birds B saw. The third yellow bird B saw could not have been the one A and B saw together, because A only saw two yellow birds; so the third yellow bird B saw must have been the one he saw alone.
So five yellow birds were seen (the one B saw, the one C saw, the one A and C saw, the one B and C saw, and the one all three saw), and two non-yellow birds were seen (the one A saw and the one A and B saw) by the group.
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