A simple riddle many people miss - the watermelon paradox

Summary

In this intriguing video, Press Tow Walker presents a popular riddle involving watermelons with a water content of 99% that, after evaporation, drops to 98%. The challenge is to determine the final weight of the watermelons, which surprisingly turns out to be 50 kg, contrary to the initial intuitive guess of 99 kg. The video explores various methods to solve the puzzle, revealing a veridical paradox—a counterintuitive yet correct result—and encourages viewers to share the puzzle to witness others' surprising reactions.

Takeaways

• 🍉 The presented riddle involves watermelons with an initial water content of 99% that decreases to 98% by the time they reach their destination.
• 🚂 The watermelons were transported by train, and the weight change is the focus of the riddle.
• 📚 This riddle is a popular puzzle that has appeared in exams like KVPY in India and might be part of technical interviews.
• 🥔 The puzzle can also be framed with potatoes instead of watermelons, but the mathematical principle remains the same.
• 🤔 The initial intuitive answer of 99 kg is incorrect, which surprises many, including educated individuals with advanced degrees.
• 🎓 Even a group of MERS and PhD scientists initially got the puzzle wrong, highlighting the counterintuitive nature of the result.
• 📉 The correct answer is 50 kg, indicating a significant loss in weight when the water content drops from 99% to 98%.
• 📝 The script explains multiple methods to solve the puzzle, emphasizing the importance of careful mathematical reasoning.
• 🔢 The solution involves understanding that the 'dry' weight remains constant while the water weight changes as a percentage of the total weight.
• 🧩 The script uses algebraic equations to demonstrate that the final weight must be 50 kg, correcting the common misconception.
• 📊 A visual representation with dots is provided to illustrate why the final weight is 50 kg, making the abstract concept more tangible.
• 🎭 The riddle is referred to as a 'veridical paradox' because it yields an absurd or counterintuitive but correct result.

Q & A

What is the riddle presented in the video about?

The riddle is about a person who carried 100 kg of watermelons with an initial water content of 99%. After traveling by train, the water content dropped to 98%, and the question is to determine the final weight of the watermelons.

Why is the intuitive answer of 99 kg incorrect?

The intuitive answer of 99 kg is incorrect because it assumes that only 1 kg of water is lost, which would be 1% of the initial 100 kg. However, this doesn't account for the change in the proportion of water to the total weight.

What is the correct final weight of the watermelons after the water content drops?

The correct final weight of the watermelons is 50 kg, which is a surprising result given the initial assumption.

What is the term used to describe the type of paradox presented in the riddle?

The term used to describe this type of paradox is a 'veridical paradox', which is a result that is absurd or counterintuitive but is actually correct.

How does the video explain the incorrect reasoning behind the initial guess of 99 kg?

The video explains that the incorrect reasoning is based on the assumption that only 1 kg of water is lost, without considering that the remaining weight must also adjust to maintain the new water content percentage.

What is the initial water content of the watermelons in the riddle?

The initial water content of the watermelons is 99%.

What percentage does the water content drop to after the journey?

The water content drops to 98% after the journey.

What is the term used for the puzzle when it involves potatoes instead of watermelons?

The term used for the puzzle when it involves potatoes instead of watermelons is not specified in the script, but it is implied that the mathematics and the principle behind the puzzle remain the same.

What is the role of the 1 kg of 'other weight' in the riddle?

The 1 kg of 'other weight' represents the non-water content of the watermelons, which remains constant throughout the journey while the water content decreases.

How does the video script illustrate the correct answer of 50 kg?

The video script illustrates the correct answer by showing that if the final weight were 99 kg with 98% water content, it would create a contradiction. It then uses algebraic methods to solve for the final weight, which turns out to be 50 kg.

What is the significance of the 100 dots visual representation in the video?

The 100 dots visual representation is used to show the initial 100 kg of watermelons, with 99 dots representing the water weight and 1 dot representing the dry weight. As water evaporates, the dry weight remains, and the final total weight is recalculated based on the new water content percentage.

Outlines

00:00

🍉 The Watermelon Riddle Puzzle

This paragraph introduces a popular riddle about watermelons with a high water content that is transported by train during summer. The riddle involves a 100 kg batch of watermelons with an initial 99% water content, which decreases to 98% by the time they reach the destination. The challenge is to determine the final weight of the watermelons. The paragraph discusses common incorrect reasoning and mentions that even educated individuals have struggled with this puzzle. It sets the stage for explaining the correct solution, which is revealed to be 50 kg, contrary to the intuitive but incorrect answer of 99 kg.

05:00

📚 Solving the Watermelon Riddle with Algebra

This paragraph delves into the correct solution of the watermelon riddle using algebraic methods. It explains the initial misconception and then provides a step-by-step algebraic approach to arrive at the correct answer. The explanation involves setting up equations based on the water content and the dry weight of the watermelons, which remains constant. The paragraph illustrates different algebraic methods to solve for the final weight, including a visual representation using dots to symbolize the weight distribution, ultimately confirming the surprising result of 50 kg.

10:01

🧠 The Veridical Paradox of the Watermelon Riddle

The final paragraph addresses potential objections to the term 'paradox' used in describing the watermelon riddle. It clarifies that a veridical paradox is a term used for results that are counterintuitive yet correct, making it appropriate for this riddle. The paragraph concludes by encouraging the sharing of the puzzle with others to observe their reactions and to prepare for discussions about the nature of paradoxes. It ends with a note of thanks to the community and a teaser for the next episode of 'Mind Your Decisions'.

Keywords

💡Riddle

A riddle is a type of puzzle that requires the solver to find the answer to a question or problem that has a double or hidden meaning, often leading to a surprising conclusion. In the video, the riddle about watermelons involves a surprising result when the water content changes, which is central to the video's theme of exploring counterintuitive outcomes.

💡Watermelons

Watermelons are large, green fruits with a high water content, often used in the context of this video as a subject for the riddle. The script uses watermelons to illustrate a mathematical problem involving weight loss due to water evaporation, which is a key element in the puzzle presented.

💡Water Content

Water content refers to the percentage of water in a substance. In the video, the initial water content of the watermelons is 99%, and it drops to 98% by the end of the journey, which is the main factor in the weight change of the watermelons and the crux of the riddle.

💡Weight

Weight is a measure of the force exerted on a mass of an object due to gravity. The video script discusses the change in weight of the watermelons from 100 kg to a final weight, which is the ultimate answer to the riddle.

💡Evaporation

Evaporation is the process by which water changes from a liquid to a gas or vapor. In the context of the video, the evaporation of water from the watermelons is what causes the change in their water content and, consequently, their weight.

💡Percentage

A percentage is a way of expressing a number as a fraction of 100. It is used in the video to describe the water content of the watermelons both initially (99%) and at the end (98%), which is essential for solving the riddle.

💡Puzzle

A puzzle is a game, question, or problem designed to test ingenuity or knowledge. The video presents a mathematical puzzle involving the weight and water content of watermelons, which is meant to challenge the viewer's problem-solving skills.

💡Paradox

A paradox is a statement or situation that seems self-contradictory or absurd but in reality expresses a possible truth. The video refers to the surprising result of the riddle as a 'veridical paradox,' highlighting the unexpected nature of the solution.

💡Dry Weight

Dry weight refers to the weight of an object excluding the weight of water it contains. In the script, the dry weight of the watermelons remains constant at 1 kg, which is a critical factor in determining the final weight after the water has evaporated.

💡Algebraic Method

An algebraic method is a mathematical approach that uses algebra to solve problems. The video explains multiple algebraic methods to solve the riddle, including setting up equations to represent the relationship between the initial and final weights of the watermelons.

💡Visualization

Visualization is the process of creating images or diagrams to represent data or concepts. The video uses a visual representation of dots to illustrate the water and dry weight of the watermelons, helping to make the abstract concept of percentage weight change more concrete.

Highlights

Press Tow presents a popular riddle involving watermelons with a water content of 99% that decreases to 98% during transit.

The riddle appeared on an exam in India called KVPY and is also a common interview question.

The intuitive but incorrect answer is that the watermelons weigh 99 kg after the water content drops.

The puzzle is known to stump even highly educated individuals, including PhD scientists.

The correct answer to the riddle is that the watermelons weigh 50 kg after the water content change.

The explanation involves understanding that the 'dry weight' remains constant while the water weight changes.

A step-by-step algebraic solution is provided to demonstrate why the watermelons weigh 50 kg.

The explanation uses the concept of percentages and algebra to solve the riddle.

A contradiction arises when assuming the final weight is 99 kg, leading to the realization that the weight must be less.

The final weight is found by setting up an equation where the dry weight plus water weight equals the total weight.

The riddle is solved by understanding that the loss in weight is due to the evaporation of water, not the dry matter.

A visual representation using dots helps to illustrate why the final weight is 50 kg.

The riddle is an example of a veridical paradox, where the result is counterintuitive but correct.

The video encourages viewers to share the riddle to observe others' reactions to the surprising answer.

The video concludes by emphasizing the importance of basic mathematics in solving the riddle.

The video is part of the 'Mind Your Decisions' series, which aims to solve the world's problems one video at a time.

Transcripts

hey this is press tow

Walker so here's a really fun riddle I

carried 100 kg of watermelons in the

summer by train in the beginning their

water content was

99% by the time I reached the

destination the water content had

dropped to

98% in the end how much did the

Watermelons

weigh this is a very popular puzzle a

version of it appeared on an exam in

India called the kvpy and I wouldn't be

surprised if appeared in many other

places like other exams or even

technical interview

questions you may also have seen this

puzzle in terms of potatoes instead of

watermelons but nonetheless the

mathematics are the same so I returned

to the original problem in the end how

much did the watermelons

way pause the video if you'd like to

give this problem a try and when you're

ready keep watching to learn how to

solve this

problem so at first glance this puzzle

seems like a piece of cake ha what's the

big deal the answer is easy the

Watermelons obviously weigh 99

kg so if someone gives this answer you

might ask how did you reason

so here's how the reasoning often goes

well the water content was 99% in the

beginning in the end the water content

dropped to

98% so that would be a loss of 1% of

water the weight at the beginning was

100 kg so a loss of 1% of 100 will be 1

kg therefore the final weight will be 99

% of 100 kg which equals 99 kg piece of

cake so unfortunately this intuitive

answer of 99 kg is wrong not only is it

wrong it's not even close to the answer

but don't worry if you got the wrong

answer you're in very good company a

blog post by Cambridge coaching explains

that this puzzle was given at a barbecue

with several m MERS and PhD scientists

and they all came up with the wrong

answer of 99 kg the post wondered how

can several people most of whom have a

PhD in science or at the very least a

master's in it get this wrong they

weren't even close to the correct answer

they were really off I mean these are

smart accomplished people and I'm not

saying that just because they are my

friends what's more interesting is that

when told their answer was wrong and

after spending a few minutes thinking

about it it everyone got the right

answer so what is the right answer it is

50 kg you lose a surprising half of the

weight when the water content drops from

99% to

98% so since the answer is so surprising

let's work out carefully why the answer

is 50 kg I'll explain a few different

methods so let's get started with one so

in the beginning there's a 100 kg of

weight

we know that water is 99% of this weight

which means that 99 kg is water and the

remaining 1 kg is other weight you could

call it dry weight now what happens at

the end we don't know the weight at the

end that's what we want to solve for but

we do know the water content is

98% what else do we know we know that

the water evaporates but the 1 kg of

other weight has to remain the same so

we take this 1 kg of other weight and we

bring it to the

end so now let's imagine that the final

weight was 99 kg as everyone initially

thinks so what would happen if it were

98% Water by weight

99.98 is equal to

97.0 let's just round that to 97 kg

so in this case we actually end up with

a contradiction if we sum up the weight

of 97 and 1 we get a total of 98 kg but

wait we said that the total was supposed

to be 99 kg so it's not possible that

the weight is 99 kg this would create a

contradiction so what is the correct way

to solve this problem so let's suppose

the final weight is equal to the

variable

W since we have 98% weight by water we

want the water weight to be

98w kg of

water we now need the weight at the end

to be equal to the weight w so we want

98 W + 1 to be equal to the original

weight of w this gives the equation W is

equal to 98 W +

1 we'll solve this equation for w

subtract 98 W from both sides w -98 w is

equal to 02 W this equals 1 divide both

sides by

02 and that gives the answer that W is

equal to 50 so the initial weight has to

be 50 kg so let's just go through the

calculation and make sure it

works if the ending weight is 50 kg then

9 98% of that will be 49 kg so that's

how much water weight there is we now

have 49 + 1 which equals 50 kg and that

exactly matches the 50 kg therefore 50

kg is the correct answer so let me just

illustrate the answer algebraically let

X be the final weight D be the final dry

weight and W be the final water weight

we know that the final dry weight will

be 1% of the original weight of 100

which equals 1 kg the final water weight

has to be 98% of the final weight X so

this is

98x so we have the equation that X is

equal to D + W it's the dry weight plus

the water weight we can substitute in

that W is equal to

98x and D is equal to 1 we solve this

equation for x subtract 98x from both

sides to get 02x is equal to 1 divide

through by .02 and we get that X is

equal to 50 kg but here's another

algebraic way to solve it let's consider

the weight that is lost say that's the

variable

L we know the final weight will be 100

which is the original weight minus L

then we have S as the starting water

weight which we know is equal to 99% of

100 which equals 99

kg what is the final water weight F this

will be equal to 98 98% of the final

weight and the final weight is 100 minus

l so the weight loss will be equal to

the starting water minus the final water

we substitute in four of these variables

and now we just need to solve for l so

we distribute the 98 through now we just

simplify 99 - 98 is equal to 1 then we

subtract 98 L from both sides and

finally we divide through by 02 to get

that L is equal to 50 kg so the loss is

50 kg and we take 100us 50 to equal 50

therefore the final weight is 50

kg here's a final way to visualize this

riddle we have a 100 dots that represent

a 100

kg we know that 99% is water weight so

that would be 99 dots so the remaining

one dot would represent the dry weight

so we have 99% as the water weight and

1% as the dry

weight as the water evaporates from the

beginning to the end nothing happens to

the dry weight so this dry weight gets

carried over to the

end we now need the water weight to be

98% of the total weight and the dry

weight to be 2% of the total weight so

if we have 1 kilg and we need that to

rep represent 2% we take 1 / 2% which

equals 50 kg so this would represent 50

kog so we need a total of 50 Dots here

and this represents a visual way to see

that we have 50 kilog in the

end so this is truly a remarkable riddle

and at the heart of it is just basic

mathematics so I hope you share this

puzzle with others and you'll be

surprised to see how many people are not

able to get the answer at first

guess but I want to prepare you for one

more

situation the very person who did not

get the puzzle correct will then come at

you with well this isn't a true Paradox

after all you call it the watermelon

Paradox or the potato Paradox it's not a

contradiction at all this is just a

surprising result well let me tell you

this is what's known as a veridical

paradox which is a result that is absurd

or counterintuitive but is actually

correct therefore it is appropriate to

apply the term Paradox to it and if you

have any objection to that just take it

up with

Wikipedia thanks for making us one of

the best communities on YouTube see you

next episode of mind your decisions

where we solve The World's problems one

video at a time

oh

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