## Sunday, November 13, 2005

### Any bird watchers out there?

Abel, Mabel, and Calib 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 Abel saw, two were yellow. Of the birds Mabel saw, three were yellow. Of the birds Calib saw, four were yellow. How many yellow birds were seen in all? How many non-yellow birds were seen in all?

1. 4 yellow birds
3 non-yellow

2. Three birds were seen by one person each, three were seen by each unique pair (Abel-Mabel, Abel-Calib, and Mabel-Calib), 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 Calib saw were yellow. These four birds are: (1) the one Calib saw alone, (2) the one Calib saw with Abel, (3) the one Calib saw with Mabel, and (4) the one all three saw together. This accounts for both of the yellow birds Abel saw, and two of the three yellow birds Mabel saw. The third yellow bird Mabel saw could not have been the one Abel and Mabel saw together, because Abel only saw two yellow birds; so the third yellow bird Mabel saw must have been the one she saw alone.

So five yellow birds were seen (the one Mabel saw, the one Calib saw, the one Abel and Calib saw, the one Mabel and Calib saw, and the one all three saw), and two non-yellow birds were seen (the one Abel saw and the one Abel and Mabel saw) by the group.

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