The Bird Watching Program Puzzle : Solution

What was the puzzle?

Let's find the total count of birds including yellow and non-yellow.

1. Each of them saw one bird that none of the others did. Individuals - Abel, Mabel, and Caleb. So, Birds = 3.

2. Each pair saw one bird that the third did not. Pairs - Abel-Mabel, Abel-Caleb, and Mabel-Caleb. So, Birds = 3.

3. And one bird was seen by all three. Abel-Mabel-Caleb. Birds = 1.

Therefore, total of 3 + 3 + 1 = 7 birds were seen.

It's clear that, everyone saw 4 birds viz. one individually, two when in pairs and 1 with all along. 

Since Caleb saw 4 yellow birds, Caleb must not had saw any of non-yellow birds.

The 4 yellow birds that Caleb saw must be as below.

1. The one Caleb saw individually. 

2. The one that Caleb saw in pair with Abel-Caleb.

3. The one that Caleb saw in pair with Mabel-Caleb. 

4. The one that Caleb saw with all.

Now, the two yellow birds that Abel saw must be the one that is pointed by (2) above and other pointed by (4) above.

That's make sure that the pair Abel-Mabel saw a non-yellow bird. 

Since Mabel saw 3 yellow birds, 2 of them are as pointed by (3) and (4) above, the third one must be the yellow bird that she saw alone. So far, we discovered there must be 5 yellow birds (4 seen by Caleb and one seen by Mabel individually) at least.

So, far we know Abel saw a yellow bird as in pair Abel-Caleb, one more yellow bird with all and a non-yellow bird as in pair Abel-Mabel. Hence, the fourth bird that Abel saw must be a non-yellow bird since as per data Abel saw only 2 yellow birds.