### Brain Teasers

# Stone Bridge Crossing

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 travelling 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.

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 travelling 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.

### Hint

15 steps### Answer

Step 1: Tim jumps to occupy the empty stone.Step 2: Tim helps Jen in occupying the newly emptied stone between him and Jim.

Step 3: Ben occupies the stone emptied by Jen.

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

Right now they are lined up like this:

Ann Tim Ben emp Jen Jim Kim

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

Step 6: Kim occupies the stone emptied by Jim.

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

Step 8: Jim helps Ben in occupying the stone vacated by Jen.

Now the people are lined up as follows:

Ann Tim emp Jim Ben Kim Jen

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

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

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

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

So now the people are lined up as follows:

Tim Jim Ann Kim Ben emp Jen

Step 13: Ben occupies the empty stone.

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

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

So finally the people are lined up as:

Tim Jim Kim emp Ann Ben Jen

Just as we wanted.

There are other possible answers which are permutations of the above procedure by altering certain movements, but this is one of the shortest ways.

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## Comments

I really enjoyed this! Good Job!!!

I know this exept with sheep

Thanks Dishu, Several variations of this puzzle, usually starting from each bank to find the fewest number of jumps required for all to cross.

Yes I tried many variations and this was the least no. of steps I could get. if you can achieve the result in fewer steps feel free to correct the teaser.

At first I thought, "how could this be possible? 7 spaces and 6 people." I coudn't get it, then I rembered that they could skip two at a time, then I got it.

Thanks Dishu.

Thanks Dishu.

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