The Bird Watching Program : Puzzle

Abel, Mabel, and Caleb 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 Caleb saw, four were yellow. 

How many yellow birds were seen in all? How many non-yellow birds were seen in all?

Click here for SOLUTION! 

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. 

Crossing The Stone Bridge : Puzzle

Three people, Ann, Ben and Jen want to cross a river from left bank to right bank. Another three people, Tim, Jim and Kim want to cross the same river from right bank to left bank.

However, there is no boat but only 1 stone bridge consisting of just 7 big stones(not tied to each other), each of which can hold only 1 person at a time. All these people have a limited jumping capacity, so that they can only jump to the stone immediately next to them if it is empty.
 
Now, all of these people are quite arrogant and so will never turn back once they have begun their journey. That is, they can only move forward in the direction of their destination. They are also quite selfish and will not help anybody traveling in the same direction as themselves.

But they are also practical and know that they will not be able to cross without helping each other. Each of them is willing to help a person coming from opposite direction so that they can get a path for their own journey ahead. With this help, a person can jump two stones at a time, such that if, say, Ann and Tim are occupying two adjacent stones and the stone next to Tim on the other side is empty, then Tim will help Ann in directly jumping to that stone, and vice versa.

Now initially the 6 people are lined up on the 7 stones from left to right as follows:

Ann Ben Jen emp Tim Jim Kim
(where emp stands for empty stone).

Your job is to find how they will cross over the stones such that they are finally lined up as follows:

Tim Jim Kim emp Ann Ben Jen

Now, find out the shortest step-wise procedure, assuming that Tim moves first.

THIS is the shortest way! 

Crossing The Stone Bridge Puzzle : Solution

What was the puzzle?

Initially the 6 people are lined up on the 7 stones from left to right as follows:
Ann Ben Jen EMP Tim Jim Kim
(where EMP stands for empty stone).

Step 1: Tim jumps to occupy the empty stone.

Ann Ben Jen Tim EMP Jim Kim

Step 2: Tim helps Jen in occupying the newly emptied stone between him and Jim. 

Ann Ben EMP Tim Jen Jim Kim
 
Step 3: Ben occupies the stone emptied by Jen.

Ann EMP Ben Tim Jen Jim Kim

Step 4: Ben helps Tim in occupying the newly emptied stone. 

Ann Tim Ben EMP Jen Jim Kim

Step 5: Jen helps Jim in occupying the empty stone. 

Ann Tim Ben Jim Jen EMP Kim

Step 6: Kim occupies the stone emptied by Jim. 

Ann Tim Ben Jim Jen Kim EMP

Step 7: Kim helps Jen in occupying the stone vacated by her. 

Ann Tim Ben Jim EMP Kim Jen
  
Step 8: Jim helps Ben in occupying the stone vacated by Jen. 

Ann Tim EMP Jim Ben Kim Jen

Step 9: Tim helps Ann in occupying the empty stone.

EMP Tim Ann Jim Ben Kim Jen

Step 10: Tim jumps to the stone emptied by Ann.

Tim EMP Ann Jim Ben Kim Jen

Step 11: Ann helps Jim in occupying the stone vacated by Tim.

Tim Jim Ann EMP Ben Kim Jen

Step 12: Ben helps Kim in occupying the stone vacated by Jim. 

Tim Jim Ann Kim Ben EMP Jen

Step 13: Ben occupies the empty stone.

Tim Jim Ann Kim EMP Ben Jen

Step 14: Kim helps Ann in occupying the stone emptied by Ben. 

Tim Jim EMP Kim Ann Ben Jen

Step 15: Kim jumps to the stone emptied by Ann.

Tim Jim Kim EMP Ann Ben Jen

This is exactly what we wanted!