Problem 1 I found on this puzzle 'Watermelon Paradox' on the Mind Your Decisions YouTube channel which cites the original source as the 2010 Indian KVPY exam, but it is probably a classic problem; I found 3,570 Google hits for it. It runs like this (my paraphrase)
I have 100 kg of watermelons which are initially 99% water. After a few days they have lost some moisture and are now only 98% water. How much do they weigh at this point?
Problem 2 This one is very common, with 169,000 Google hits, and I don't know where it originated. It popped up earlier this year and the Mirror wrote of it 'Incredibly hard 1% Club question leaves Brits arguing over the answer' [1]. Here is how this one goes (my paraphrase again).
In a room are 100 people, of whom 99% are left-handed. How many left-handers must leave the room to make the proportion of left-handers drop to 98%?
These two problems are the same really, only the way they are framed is different. In each there is an answer we might immediately jump to, but which on reflection turns out wrong. This is quite a good example of the System 1 thinking, as described in the 2011 book Thinking Fast and Slow by Kahneman [2]. The book contrasts two modes of thinking
System 1 is fast and intuitive, a snap answer that takes little effort to arrive at and which we don't really have to think about.
System 2 is slow and takes effort, we have to think about how to solve the problem and work the answer out methodically.
Both these systems have their place. We often must make quick judgements and much of daily life is governed by small familiar decisions taken unconsciously and here System 1 is needed. But other decisions may concern problems that are complex and unfamiliar, with answers that are unintuitive. Here System 2 is required.
Both the problems I have given above trick us into System 1 thinking, so we are tempted to say 99 kg, or 1 person. The correct answers are highly unintuitive; 50 kg and 50 people, which is quite surprising. Especially with Problem 2 I find the answer hard to believe even though I know it's right.
Here is my System 2 analysis of the two problems side by side, so you can see how they parallel one another.
These Two Problems Are Really The Same
Problem 1
I found on this puzzle 'Watermelon Paradox' on the Mind Your Decisions YouTube channel which cites the original source as the 2010 Indian KVPY exam, but it is probably a classic problem; I found 3,570 Google hits for it. It runs like this (my paraphrase)
I have 100 kg of watermelons which are initially 99% water. After a few days they have lost some moisture and are now only 98% water. How much do they weigh at this point?
Problem 2
This one is very common, with 169,000 Google hits, and I don't know where it originated. It popped up earlier this year and the Mirror wrote of it 'Incredibly hard 1% Club question leaves Brits arguing over the answer' [1]. Here is how this one goes (my paraphrase again).
In a room are 100 people, of whom 99% are left-handed. How many left-handers must leave the room to make the proportion of left-handers drop to 98%?
These two problems are the same really, only the way they are framed is different. In each there is an answer we might immediately jump to, but which on reflection turns out wrong. This is quite a good example of the System 1 thinking, as described in the 2011 book Thinking Fast and Slow by Kahneman [2]. The book contrasts two modes of thinking
System 1 is fast and intuitive, a snap answer that takes little effort to arrive at and which we don't really have to think about.
System 2 is slow and takes effort, we have to think about how to solve the problem and work the answer out methodically.
Both these systems have their place. We often must make quick judgements and much of daily life is governed by small familiar decisions taken unconsciously and here System 1 is needed. But other decisions may concern problems that are complex and unfamiliar, with answers that are unintuitive. Here System 2 is required.
Both the problems I have given above trick us into System 1 thinking, so we are tempted to say 99 kg, or 1 person. The correct answers are highly unintuitive; 50 kg and 50 people, which is quite surprising. Especially with Problem 2 I find the answer hard to believe even though I know it's right.
Here is my System 2 analysis of the two problems side by side, so you can see how they parallel one another.
[1] https://www.mirror.co.uk/news/weird-news/incredibly-hard-1-club-question-34387903
[2] https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow