A World Class Swimmer's Puzzle

A world-class swimmer can swim at twice the speed of the prevailing tide.

She swims out to a buoy and back again, taking four minutes to make the round-trip.

How long would it take her to make the identical swim in still water?

Click here for the answer!

Solution of A World Class Swimmer's Puzzle

What was the puzzle?

 Let C be the speed of water current then the speed of a world class swimmer will be 2C.

When she swims out to a buoy located at a distance say D and back again, the time needed is - 

D/(C+2C) + D/(2C-C) = 4 minutes

D/3C + D/C = 4

Multiplying both the sides by 3, 

D/C + 3D/C = 12

4D/C = 12

D/C = 3  

Now when she swims out to a buoy and back to shore again in still water, she needs only time -

D/2C + D/2C 

Since D/C = 3, then D/2C = 3/2

Hence, 
 
D/2C + D/2C  = 3/2 + 3/2 = 3.

That is, she needs only 3 minutes to swim out to a buoy and back to shore again in still water.

 
 

The Jungle On The Plot of Land

There is a plot of land that is 16 square acres, arranged in a 4 X 4 grid. There are 16 mammals, two each of the following: beaver, cat, dog, goat, horse, lion, tiger, and walrus. There is one mammal in each acre. The acres are labeled A through P, as shown below.

A B C D
E F G H
I J K L
M N O P

Given the following clues, determine where each mammal is located. The terms "next to" and "connected together" mean vertically, horizontally, or diagonally.

1) A and D do not contain the same mammal, but one of them has a dog.

2) E and O do not contain the same mammal, but one of them has a horse.

3) B and L contain the same mammal, but not a tiger.

4) C and M contain the same mammal, but not a beaver.

5) F, K, N, and P are four different mammals.

6) The tigers are in different columns.

7) The goats are located in two of the following locations: B, C, K, and O.

8) The lions are located in two of the following locations: A, E, F, and M.

9) Cats don't get along with dogs, so neither cat is next to a dog.

10) Tigers have goats on their menu, so each tiger must be next to at least one goat and each goat must be next to at least one tiger.

11) The beavers and walruses live on the same body of water, so all four must be connected together in some fashion.

Click to know how animals are located! 

Oraganised Jungle On The Plot of Land

What was the puzzle?

As per given data - 

There is one mammal in each of 16 acres arranged in 4 x 4 grids. The acres are labeled A through P, as shown below.

A B C D
E F G H
I J K L
M N O P

Given the following clues, determine where each mammal is located. The terms "next to" and "connected together" mean vertically, horizontally, or diagonally.

1) A and D do not contain the same mammal, but one of them has a dog.

2) E and O do not contain the same mammal, but one of them has a horse.

3) B and L contain the same mammal, but not a tiger.

4) C and M contain the same mammal, but not a beaver.

5) F, K, N, and P are four different mammals.

6) The tigers are in different columns.

7) The goats are located in two of the following locations: B, C, K, and O.

8) The lions are located in two of the following locations: A, E, F, and M.

9) Cats don't get along with dogs, so neither cat is next to a dog.

10) Tigers have goats on their menu, so each tiger must be next to at least one goat and each goat must be next to at least one tiger.

11) The beavers and walruses live on the same body of water, so all four must be connected together in some fashion. 

STEPS : 

1] As per Hint 3, blocks B & L contains the same mammal.  As per Hint 4, blocks C & M have the same mammal. So, as per Hint 7 suggests, the goats must be in K & O because if they are in B & C then L & M also supposed to have them but there are total 2 goats only. K - GOAT, O - GOAT

2] If O has a goat then as per Hint 2, E must have a horse.  E - HORSE

3] As per Hint 8, if Lion is located at M then as per Hint 3 the second lion must be in B. But Hint 8 doesn't list B as possible location of lions. Hence, it must not be in M. Also, E is already occupied by horse, hence lions must be at A & F.
A - LION, F - LION

4] So if A has lion, then as per Hint 1, D must have a dog. D - DOG

5] Since C is just near to the D having a dog, as per Hint 9, C can't have cats. As per Hint 10, tigers should be in the 3x3 grids around the goats and goats are located at K and O. But M is out of these grids, hence must not have tigers.

6] And as per Hint 4, C & M having same mammal, but not beaver. As deduced above, it can't be cats or tigers either. With 1 dog already at D, 1 Horse at E, both C & M can't have dogs or horses. Hence, C & M must have walruses (only left mammal out of 8 kind of mammals). C - WALRUS, M - WALRUS

7] As per Hint 11, for walruses (at C & M) to be connected with beavers in some fashion, they must be at G and J. So, G & J have beavers.
G - BEAVER, I - BEAVER

8] Since Hint 3 suggests that B & L are not having tigers, the only animals left in terms of numbers of 2 for to be at B & L are cats. So B & L have cats. B - CAT, L - CAT

9] So far, we have, A - Lion, B - Cat, C - Walrus, E - Horse D - Dog, F - Lion, 
G -  Beaver, J - Beaver, K - Goat, L -  Cat, M - Walrus, O - Goat. Blocks left are  H, I, N, P

10] As per Hint 10 & with goats at K and O, tigers can't be at I. So possible blocks for tigers are H, N and P.

11] But as per Hint 6, tigers has to be in different columns and H & P are in the same column. Also, as per Hint 5, N & P can't have same mammals. And since, H & P falls under same column, the tigers must be occupying N and H. 
 H -  TIGER, N - TIGER

12] Since one cat is at L, P can't be a dog. Hence, I must be having a dog and P must be having a horse.  I - DOG, P - HORSE.

SUMMARY : 

A = lion, B = cat, C = walrus, D = dog
E = horse, F = lion, G = beaver, H = tiger
I = dog, J = beaver, K = goat, L = cat
M = walrus, N = tiger, O = goat, P = horse

 

The Water Jug Challenge : Puzzle

You've got a 4 liter jug and a 9 liter jug. 

You've got a pool of water. 

What is the fewest number of steps it takes to come up with exactly 6 liters of water? 

No, you cannot pour some water into the 9 liter jug and then guess. Nor can you fill each jug up half way or something. You have to be exact. A step is defined as putting water into a jug (not emptying). For instance, filling the 4 liter jug and then pouring it into the 9 liter jug is 2 steps.

Click here for SOLUTION! 

The Water Jug Challenge Puzzle : Solution

What was the puzzle?

We've got a 4 liter jug and a 9 liter jug. 

We've got a pool of water. 

We have to find fewest number of steps it takes to come up with exactly 6 liters of water. 

STEPS : 

1. Fill up the 9 liter jug from the pool.         9L - 9  4L - 0

2. Fill up the 4 liter jug from the 9 liter jug. 9L - 5  4L - 4

3. Empty the 4 liter jug into the pool.          9L - 5  4L - 0

4. Fill 4 liter jug again from the 9 liter jug.   9L - 1  4L - 4

5. Empty the 4 liter jug into the pool           9L - 1  4L - 0

6. Transfer 1 liter left 9L jug into the 4L.     9L - 0  4L - 1

7. Fill the 9 liter jug from the pool.             9L - 9  4L - 1

8. Fill up the 4 liter jug from the 9 liter jug. 9L - 6  4L - 4

That's how we have exactly 6 liters of water in 9 liters jug. 

Make it 50-50 in Two!

You have three jugs:

A 10-liter jug, filled with water
A 7-liter jug, empty
A 3-liter jug, empty

Your objective is to end up having 5 liters of water in the 10-liter jug, and 5 liters of water in the 7-liter jug.

Note that you have nothing else at your disposal other than these three jugs and that you cannot perform measurements by eye or based on the shape of the jugs.

THIS is how it can be done! 

Making it 50-50 in Two!

What was the challenge?

Let us label the 10-liter jug as A, the 7-liters jug as B, and the 3-liters jug as C.

 
STEPS : 

1]  Pour Jug A into Jug C.      A : 7    B : 0    C : 3
 
2]  Pour Jug C into Jug B.      A : 7    B : 3    C : 0

3]  Pour Jug A into Jug C.      A : 4    B : 3    C : 3

4]  Pour Jug C into Jug B.      A : 4    B : 6    C : 0

5]  Pour Jug A into Jug C.      A : 1    B : 6    C : 3

6]  Pour Jug C into Jug B.      A : 1    B : 7    C : 2

7]  Pour Jug B into Jug A.      A : 8    B : 0    C : 2

8]  Pour Jug C into Jug B.      A : 8    B : 2    C : 0

9]  Pour Jug A into Jug C.      A : 5    B : 2    C : 3

10] Pour Jug C into Jug B.     A : 5    B : 5    C : 0

Task Completed.

The Watermelon Paradox

There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.

How much water evaporated?

The calculation is TRICKY one! 

Tricky Watermelon Water Weight Calculation

What is the question?

Initially, since 99% of watermelon is water, the weight of water must be 99 pounds and weight of other stuffs should be 1 pound.

After evaporation, 98% of watermelon is water indicates that the there is 2% of other stuff present at the point of time. 

That is, if we assume the weight of other stuff unchanged during evaporation, now 1 pound itself is equal to the 2% of total weight of watermelon.

In other words, the process of evaporation increased percent weight of other stuffs in total weight of watermelon from 1% to 2%.

If W is the total weight of watermelon, then weight of other stuffs (which is 1 pound)

W x (2/100) = 1 pound

W = 50 Pounds.

Out of these 50 pound, 1 pound (2% of total weight) is other stuffs and 49 pounds is water (98% of total weight).

That means, out of 99 pounds of water, 99 - 49 = 50 pounds of water is evaporated in the process. 

The Poisonous Glass?

You are given 4 identical glasses, completely filled with transparent, odorless liquids. Three of the liquids are pure water, and the fourth is poison, which is slightly heavier. If the water glasses weigh 250 grams each, and the poisoned glass weighs 260 grams, how can you figure out which one is which, using a measuring scale just once?

Here is the process to identify the poisonous glass!

Identifying The Poisonous Glass!

What was the challenge?

Let's number the 4 glasses as 1,2,3 and 4.

Here are steps to identify the glass with poisonous liquid in it. 

1. Empty the glass 1 into another empty glass.

2. Take about 1/4th liquid from glass 2 and pour it into emptied glass 1.

3. Take 3/4th of liquid from glass 3 and pout it into glass 1.

Now, glass 1 has 1/4th of liquid from glass 2 and 3/4th from glass 3.

4. Now put glass 1 and glass 4 on the measuring scale.

    4.1 - If it weighs exactly 500 gm then it suggests that glass 1 had poison.
  
    4.2 - If it weighs between 500 - 505 grams (precisely 502.5 if exactly 1/4th of liquid was taken from glass 2 to glass 1) then obviously glass 2 is with poisonous liquid.

    4.3 - If it weighs between 505 - 510 grams (precisely 507.5 if exactly 3/4th of liquid was taken from glass 3 to glass 1) then obviously glass 3 is with poisonous liquid.

    4.4 - If it weighs exactly 510 gm then it suggests that glass 4 has poison.

 

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.  

How it Will Affect the Water Level?

A man stuck in a small sailboat on a perfectly calm lake throws a stone overboard. It sinks to the bottom of the lake.

When the water again settles to a perfect calm, is the water level in the lake higher, lower, or in the same place compared to where it was before the stone was cast in?

Did you think it will rise? 

Physics : Finding the Effect on the Water Level

But why water level was affected?

Do you recall what does Archimedes Principle state? For an object to float on water, it has to displace that much volume of water whose weight is equal to weight of the object itself. Now if object has less density than water then obviously it has to displace lesser amount of volume of water to float on it. That means it has to sink less in water.

For a moment, let's assume the stone has very high density & hence having weight equal to hundreds of kilograms despite of having small volume.

Here, stone sinks to the bottom of the lake suggests that it is has more density than water. It can't displace the water whose weight is equal to it's weight.But when it was on sailboat it could push the sailboat down so that more water is displaced weighing equal to it's weight. Result of this, the sailboat sinks little 'deeper' compared to when stone wasn't there.

Obviously, the volume of displaced water when stone was in sailboat (due to stone only) must be greater that the volume of displaced water when stone sinks to the bottom of the lake. That's why both sailboat and stone together could float on the water. In short, sailboat helped stone to displace amount of water needed to float which results in rise in shoreline.

And when stone is thrown out of the sailboat, then ideally it can't displace more water than when it was on sailboat. Now, sailboat sinks less 'deeper' in water displacing only water need to float itself. 

That's why the water level must be dropped compared to earlier. The little rise due to water displaced by stone can't exceed the earlier water level for the reason explained above.

Draining Reservoir

A large fresh water reservoir has two types of drainage system: small pipes and large pipes.

6 large pipes, on their own, can drain the reservoir in 12 hours.

3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.

How long will 5 small pipes, on their own, take to drain the reservoir?

Find here the exact time required! 

Time To Drain The Reservoir

Here is the question! 

Let T be the capacity of the tank. Let L be the large pipe and S be the small pipe.

T/6L = 12

L = T/72

T/(3L + 9S) = 8

Putting L = T/72,

S = T/108

Hence T/5S = 108/5 gives S = 21.6 hours.

To conclude, small pipes require 21.6 hours i.e. 21 hours and 36 minutes to drain the reservoir.

Fair Distribution Of Water

In Sahara desert , 3 men found a big 24L Jar is full of water. Since there is shortage of water so they decided to distribute the water among themselves such that they all have equal amounts of it. But they only have a 13L, a 5L and an 11 liter Jar.

How do they do it? 

Here is how to do it!

Source 

Equal Distribution Of Water

What was the challenge?

1. First pour 24L into 13L and 11L jar.There will be no water in 24L jar.

2. Now pour 13L jar into 5L jar till 5L is filled. So 8L of water will be left in 13L jar.

3. This 8L of water from 13L jar is emptied in empty 24L jar.This will leave 13L jar empty.

4. Now pour 11L water from 11L jar into 13L of jar. There is still space for 2L of water in 13L jar.

5. Pour 5L jar into 13L of jar which had space for 2L only. So 3L of water will be left in 5L of jar.

6. This 3L of water is emptied in 11L jar.

7. A 13L jar full of water is again poured into 5L jar leaving behind 8L of water in it.

8. A 5L jar full of water is finally poured in 11L jar already having 3L of water. 

9. This way, 24L, 11L and 13L of jar would have 8L of water each.