Row Row Row A Tiny RowBoat : Puzzle

Walter, Xavier, Yoshi, and Zeke crossed a river in a tiny rowboat. They all started on the same side of the river. They made three trips from the starting side to the destination side, and two trips from the destination side to the starting side. Here are some facts:

1. On each trip from the starting side of the river to the destination side, two people were in the boat, but only one person rowed the boat, and that person rowed the boat for the entire trip.

2. On each return trip, only one person was in the boat.

3. Walter is the weakest of the group. He could only row the boat if no one else is in it.

4. Xavier is the second weakest of the group. He can only row the boat if he is by himself or if Yoshi, the lightest of the group, is a passenger.

5. Each man rowed the boat at least once. 

Click here for SOLUTION! 

Row Row Row A Tiny RowBoat Puzzle : Solution

What was the puzzle?

We know, Walter, Xavier, Yoshi, and Zeke crossed a river in a tiny rowboat. They all started on the same side of the river. They made three trips from the starting side to the destination side, and two trips from the destination side to the starting side. 

And we have some facts:

1. On each trip from the starting side of the river to the destination side, two people were in the boat, but only one person rowed the boat, and that person rowed the boat for the entire trip.

2. On each return trip, only one person was in the boat.

3. Walter is the weakest of the group. He could only row the boat if no one else is in it.

4. Xavier is the second weakest of the group. He can only row the boat if he is by himself or if Yoshi, the lightest of the group, is a passenger.

5. Each man rowed the boat at least once. 

ANALYSIS :

1] Walter must not had rowed from start to the destination since he is weakest among as per FACT 3. Since, he had to row at least once as per FACT 5, he must had rowed a return tip.


2] The person who had rowed twice, must not had both trips from start to destination. That's because, in that case, he would have had needed third trip in form of return trip to get back to the start once again. So, he must had rowed a return trip at least once.

3] Suppose Walter is the person who rowed the boat twice. Both of his trips must be return trips as concluded in [1] above. 

So if Walter had rowed 2 return trips then each of Xavier, Yoshi and Zeke must have rowed 1 trip from start to the destination. 

If Walter had 'taken' Zeke (while Zeke rowing) across and returned then he would have had to 'take' Yoshi (while Yoshi rowing) across as Xavier being unable to row Walter as per FACT 4. And on returning back to the start after leaving Yoshi across, Walter and Xavier would have had been at the starting point. Now, Walter being unable to row with passenger & Xavier being unable to row Walter, both would have had stuck at the start point.

In short, Walter is not the person for sure who had rowed twice.

4] We know, Walter had one return trip. So the other return trip must have been rowed by someone among Xavier, Yoshi or Zeke. Moreover, the rest of three trips from start to the destination must have rowed by Xavier, Yoshi and Zeke in some order. 

That's how, the one person among Xavier, Yoshi and Zeke, must have rowed twice, one trip from source to destination and other one return trip.

5] If Xavier had rowed twice, then with one trip he must have taken Yoshi across and in other trip he must have returned as we found the fact in [2] above. So, two return trips 'occupied' by Walter and Xavier, Yoshi wouldn't have got a chance to row which is mandatory.

So, Xavier is not the person who had rowed twice.

6] Suppose Zeke is the person who had rowed twice. He must had rowed Walter across the river to give a chance to row his return trip. After Walter reaching at the start, Xavier must had rowed Yoshi across the river thereby completing his compulsory rowing trip.

Then Zeke must have returned to the start to take Walter across then Yoshi would have been the person who hadn't rowed which is against FACT 5.

Therefore, Zeke must not be the person who rowed twice.

7] So, Yoshi must be the person who rowed twice. 

POSSIBILITY 1 : Zeke took Walter across to give him row trip in return. Then, Xavier rowed Yoshi across and Yoshi returned back to take Walter across.

POSSIBILITY 2 : First Xavier rowed Yoshi across and Yoshi returned back after which Zeke takes Walter across to allow Walter to have return trip, and finally, Yoshi taking Walter across the river.

POSSIBILITY 3 : Yoshi took Walter across the river and Walter returned. Zeke rowed Walter across and Yoshi returned to give Xavier a chance to row him across.

Navigation Paths Between Two Points

Consider a rectangular grid of 4×3 with lower left corner named as A and upper right corner named B. Suppose that starting point is A and you can move one step up(U) or one step right(R) only. This is continued until B is reached. 

How many different paths from A to B possible ? 

Here is calculation of total number of paths. 

Combinations of Naviagation Paths

What is the question?

If the right move is represented as R and up move as U then, RRRUU is the one path to reach at B.

UURRR is one more path between points A and B.

URRRU is another way to reach at B.

Further, one can reach at B via RURRU.

So number of such paths are possible.

However, if all paths above are observed, we can conclude that total 5 moves are needed to reach from point A to B. Out of those 5, 3 have to be RIGHT and 2 have to be UP. 

That is, any combination having 3R and 2U in 5 moves will give a valid path to reach at B.

Now, number of ways 3R can be placed in 5 moves can be calculated as - 

C(5,3) = 5!/(5-3)! * 2! = 10.

To sum up, there are 10 paths available between points A and B.
 

The Camel and Banana Puzzle

The owner of a banana plantation has a camel. He wants to transport his 3000 bananas to the market, which is located after the desert. The distance between his banana plantation and the market is about 1000 kilometer. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels.

What is the most bananas you can bring over to your destination?

As many as 'these' numbers of bananas can be saved!

The Camel and Banana Puzzle : Solution

What was the puzzle? 

 Let A be the starting point and B be the destination in this transportation. If the camel is taken with 1000 bananas at start, to reach the point B which is 1000 km away from A, it needs 1000 bananas. So there will be no bananas left to return back to point A.

That's why we need to break down the journey into 3 parts.

Part 1 :

For every 1 km the camel needs to -

1. Move ahead 1 km with 1000 bananas but eat 1 banana in a way.

2. Leave 998 bananas at the point and take 1 banana to return back to previous point.

3. Pick up another 1000 bananas and move forward while eating 1 banana.

4. Drop 998 bananas at the same point. Return back to previous point by consuming 1 banana.

5. Pick left over 1000 bananas and move 1km forward while consuming 1 banana to same point where 998 + 998 bananas are dropped. Now, the camel doesn't need to  return back to previous point. So, 998 + 998 + 999 are carried to the point.

That is for every 1km, the camel needs 5 bananas.

After 200 km from point A, the camel eats of 200x5 = 1000 bananas and at this point the part 1 ends.

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PART 2 :

1. Move ahead 1 km with 1000 bananas but eat 1 banana in a way.

2. Leave 998 bananas at the point and take 1 banana to return back to previous point.

3. Pick up another 1000 bananas and move forward to the point where 998 bananas left while eating 1 banana.

Now, the camel needs only 3 bananas per km.

So for next 333 km, the camel eats up 333x3 = 999 bananas.

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PART 3 :

So far, the camel has travelled 200 + 333 = 533 km from point A and needs to cover 1000 - 533 = 467 km more to reach at B.

Number of bananas left are 3000 - 1000 - 999 = 1001.

Now, instead of wasting another 3 bananas for next 1 km here, better drop 1 banana at the point P2 and move ahead to B with 1000 bananas. This time the camel doesn't need to go back at previous points & can move ahead straightaway.

For the remaining distance of 467 km, the camel eats up another 467 bananas and in the end 1000 - 467 = 533 bananas will be left.

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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.