Puzzle : And Escape Story of Robbers Continues

Where story begins?

Babylas, Hilary, and Sosthenes have escaped the tower and divided their treasure into three bags. But now they must cross a river, and the boat can accommodate only two men at a time, or one man and a bag. None will trust another with his bag on the shore, but they agree that a man in the boat can be trusted to drop or retrieve a bag at either shore, as he’ll be too busy to tamper with it.

 How can they cross the river?

Source. 


This is how they can cross the river! 

 

Solution: Robbers' Planned Journey Across the River

Why they need a PLAN?

Let's recall that the boat can accommodate only two men at a time, or one man and a bag.

1. Sosthenes takes his bag across the river leaves it at other shore & comes back.

2. Sosthenes takes Hilari's bag to the other shore & leaves it there where his own bag is already there. 

3. Now, Hilari takes Sosthenes to the other shore, leaves him there & come back after recollecting own bag.

4. Hilari drops own bag at near shore & takes Babylas to other shore & returns back.

5. Next, he takes Babylas's bag & drops it at other shore where Babylas is waiting for his bag. And Hilary returns once again.

6. Finally, he collects his own bag and takes it to other shore.

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!

 

"How Did They Cross The River?"

Five men and five dogs (each man owned a dog) went hiking. They encountered a river that was swift and deep. The only way to cross it was an abandoned boat, left ashore on their side. But it would only hold three living things. 

Unfortunately, the dogs were edgy and could not be near another person (not even momentarily) unless its owner was present. One of the dogs attended a highly advanced, highly specialized obedience school and therefore knew how to operate the boat (as the men did) -- the other dogs lack this skill. 

How did the five men and the five dogs cross the river?

THIS is how they accepted the challenge! 

The Challenge of River Crossing

What was the challenge?

Let's name five men as M1, M2, M3, M4, M5 & five dogs as D1, D2, D3, D4, D5.
Assume D1 be the dog having advanced skills of operating boat.

TRAVEL CHART :

1] The dog D1 rows D2, D3 across the river and returns back. After returning back D1 takes D4 across the river & returns back once again.

START : D1-M1, D5-M5, M2, M3, M4  DESTINATION : D2, D3, D4

2] Now, M2, M3 and M4 cross river.

START : D1-M1, D1-M5  DESTINATION : D2-M2, D3-M3, D4-M4

3] Someone from DESTINATION needs to return back to allow others at START to cross the river. So, D4-M4 returns and D1-M1 cross the river. 

START : D4-M4, D5-M5  DESTINATION : D1-M1, D2-M2, D3-M3

4] After D1-M1 reaches to the DESTINATION, D3-M3 returns back.

START : D3-M3, D4-M4, D5-M5  DESTINATION : D1-M1, D2-M2

5] Now, M3, M4 and M5 cross the river.

START : D3, D4, D5  DESTINATION : D1-M1, D2-M2, M3, M4, M5.

6] Finally, the dog D1 at the DESTINATION returns back and makes 2 trips to take D3, D4 and D5 across the river.

START : None  DESTINATION : D1-M1, D2-M2, D3-M3, D4-M4, D5-M5.

This way, five men and five dog cross the river successfully.

Sara's Desert Trek

Sara needs to trek from an oasis to a destination 10 miles away across a barren desert. 

The facts:

• Crossing one mile of desert requires using 1 gallon of water.
• Sara can only carry 6 gallons of water at a time.
• Sara can drop a water cache (of any amount of water from the supply she is carrying at that moment) at any of the nine stops along the route, and then pick up any part of the cache on a later trip.

What's the minimum number of times Sara must leave the oasis in order to cross the entire 10 mile span of desert?

This is how she optimizes her journey! 

Sara's Planning in Desert Trek

What was the challenge in journey?

1. First Sara collects 12 gallons of water at milepost 1 after having 3 trips from source. She uses 2 gallons (out of 6) for forward & backward journey from source to milepost & dropping 4 gallons in cache at milepost 1.

2.She collect 6 gallons more water at the start of 4th trip from source & drops 5 gallons at milepost 1. Now, she doesn't need to return back to source and 17 gallons of water available at milepost 1.

3.In next 2 rounds, she moves 8 gallons of water from milepost 1 to milepost 2 (1 for forward + 4 for drop + 1 for backward journey in each round). 

4.Now only 5 gallons left at milepost 2. She uses 1 gallon for journey from milepost 1 to milepost 2 and drop remaining 4 gallons at milepost 2. Now, 12 gallons of water is available at milepost 2.

3.Next, using 2 gallons (out of 6 which is maximum she can carry) she moves from milepost 2 to milepost 4 and drop 2 gallons at milepost 4 & comes back at milepost 2 using remaining 2. 

4. Again, on arriving back at milepost 2, she has left with 6 gallons of water at milepost 2 out of which she uses 2 to reach milepost 4 where 2 gallons of water still available there already collected in previous round. Now, she doesn't need to return back from
milepost 4.

5. She uses the remaining 6 gallons of water to reach at the milepost 10.

To conclude, Sara has to leave Oasis only 4 times as describe in steps 1 and 2 if she want to cross the entire 10 mile span of desert.  

Crossing The River In Minimum Time

Four people need to cross a dark river at night. They have only one torch and the river is too risky to cross without the torch. If all people cross simultaneously then torch light won't be sufficient. Speed of each person of crossing the river is different. Cross time for each person is 1 min, 2 mins, 7 mins and 10 mins. 

However 2 can cross together but there is one limitation.If two are crossing the river then it takes time equal to slowest person would take alone. For example, if persons with cross times 1 min & 10 mins are crossing then it would take 10 mins for both to cross the river.

What is the shortest time needed for all four of them to cross the river ? 

  
Find here the efficient way! 

Source 

Efficient Way To Cross The River

What's the challenge? 

Let's name each person by their crossing times as 1,2,7,10.

The instant solution that everyone can think of is using 1 as a usher to guide all. That means 10 & 1 goes, 1 comes back; 7 & 1 goes again 1 comes back and 2& 1 goes finally. This would take 10 + 1 + 7 + 1 + 2 = 21 mins to cross rivers.

Is it really efficient solution? What if we find a way to cross both 10 & 7 in one go & other 1 waiting across to bring back torch.

1. The 1 & 2 goes across but 1 comes back - 2 + 1 = 3 mins required.

2. Now 10 & 7 goes across & send 2 back with torch - 10 + 2 = 12 mins required.

3. Finally after coming back 2 & take 1 across the river - 2 minutes required.

So total 3 + 12 + 2 = 17 minutes required to cross the river for those 4 persons. In first step, 2 can also come back & send 10 & 7. In that case, in second step, 1 has to come back to take 2 across the river. Isn't this a more practical solution? 

250 Lbs Across The River?

Two boys weighing 50 pounds each and their older brother weighing 100 pounds wish to cross a river. Their boat will only hold 100 pounds.

How can they all cross the river in the boat?

Find here how they can! 

Source 

Taking 250 Lbs Across The River.

What was the challenge? 

1. First 2 boys of 50 pounds should cross the river.

2. One of them should bring back the boat at other end.

3. A boy with 100 pounds should carry himself across the river with boat.

4. Other boy of 50 pounds waiting across the river now should bring back the boat again.

5. Now both boys of 50 pounds now should cross the river.