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?

Giving the birds number as to whom they were seen by makes this one easy. They each see one that others don't see, so 1,2,3. Each pair sees one that the third doesn't see, so 4,5,6. And they all see one bird 7. As follows.

A-1467
B-2457
C-3567

Since C saw four yellow ...
A-14YY
B-24YY
C-YYYY

Since A only saw two yellow, then 1 and 4 are not yellow, so
A-NNYY
B-2NYY
C-YYYY

B saw three yellow, so the last bird was yellow.

So the seven birds look like this
1-N
2-Y
3-Y
4-N
5-Y
6-Y
7-Y

The answer?
(a)5
(b)2

Posted by Lawrence on 2003-08-30 13:49:51