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120
One I haven't seen anywhere:
I go hiking on a mountain. When I start, the water makes up half the total wieght of my backpack. When I reach the summit, I have drunk half the water. What proportion of the backpack weight does it make up now?
90
You can use the questions from the Cognitive Reflection Test
- A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
- If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
- In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
The intuitive answers to these questions that "system 1" gives typically are: 10 cents, 100 minutes, and 24 days; while the correct solutions are: 5 cents, 5 minutes, and 47 days.
50
One for older / more interested kids - the Monty Hall problem.
I remember my uncle spending a long time going through this with me and having to actually run the scenario a few times for me to believe he was right!
41
Mirrors don't reflect left to right, they reflect back to front. If I make an L with my hand as seen by my POV, it'll still be an L in the mirror. However, if I write an L on a piece of paper, and then pick it up and show it to the mirror, then I've flipped the paper. That is, looking at text on a T-shirt through a mirror is like looking at the text from the inside of the shirt
I look at a restaurants reviews, and pick a 4 star restaurant (the best given my budget). When I go in, I notice that they have great music, seating, and looks. I sigh, and reduce my expectations of their food quality. Why?
The good other stuff means that the restaurant no longer needs to have unusually good food to get 4 stars, so there's not so much selection on that. So food quality is closer to average.
Suppose I uniformly randomly pick a point in the square. Whats's the probability I pick the center?
0%. It is, of course, still possible.
A barber shaves the heads of all men in his town who do not shave themselves (and only those men). Does he shave his own head?
This is known as Russell's paradox, and it shows that naive set theory is contradictory. You can try explaining a little bit about sets and then ask if the set of all sets that dont't contain themselves contains itself.
Why does evolution happen, anyways?
Things that reproduce more will have more of themselves later. Genes that lead to more children with itself in it will become more common. Nothing magical, no "bettering" force, just what is practically a tautology that the things that copy themselves more in the later generations will have more of their copies in those generations.
...so, do, say, bears have children way more than dinos did?
I think the standard answer comes from Fischer: organisms are in an 'arms race', where you have to do all this adapting and evolving just to stay at the same fitness, given that your competitors are doing so too: a Red Queen's Race.
I have a set of three 6 sided dice with numbers on the faces. We'll use them to play a game: you'll pick one die, and then I'll pick another. Then we'll roll our dice, and the highest number will win.
I must admit, however, that I'm a dirty cheater: my set of dice have the special property that I can always pick a die in response to yours that beats it on average! That is, dice A is beaten by dice B is beaten by dice C is beaten by dice A! How can this be? Can you come up with an example?
(this took adult me like a couple hours to figure out, but there are probably some kids that could do it in 10 minutes. for the most part prerequisite explicit math skills don't help for this one).
These are called intransitive dice, and they're basically the same thing as having three politicians where for every candidate, a majority always prefers a different candidate.
Which came first, the chicken or the egg?
I don't know of a standard answer to this, but ever since I was a little kid I thought the answer was obvious: at some point, a non-chicken will lay an egg with enough genetic similarity to cross whatever your 'chicken' threshold is, and thus be the progenitor of chickens. As I'd state it now: chickenhood is not a property that passes perfectly from hen to egg, for the genome of a species is made of many tiny parts that mix together.
A tree starts from a tiny seed, and grows into a huge tree. Where does the mass come from?
Almost all of it is from the air. Plants make their carbohydrates from carbon dioxide.
A dictator rules an island full of 100 green-eyed people. No person is allowed to discover what their own eye-color is via mirrors, discussion, etc. They can, however, each see that everyone else has green eyes. The only possible eye color is blue.
Every night, the dictator allows anyone who wants to leave to get into a ferry, which will take them to a refugee camp in a safe country if they have green eyes, but will kill them if they don't.
The people of this island will only attempt to leave if they are 'sure' they won't be killed. They are also all 'perfectly rational', and they all know these two facts about each other, and know that they all know those facts, and know that they all know that they all know that they know thase facts, etc.
One day, after pressure from the UN, the dictator agrees to make an announcement to the island that he believes is harmless but that the fussy humanitarians insist on him saying. The dictator, evil as he is, is known to speak only truth, and has never once lied publicly. He announces the following:
"At least one of you have green eyes".
As expected, nothing seems to happen. After all, everyone already knew that at least one person had green eyes!
However, around three months later, everyone leaves the island, certain that they have green eyes. How come?
Suppose there were 2 people on the island. If only one had green eyes, then they'd see the other had blue, and leave the first night. So if nobody leaves on the first night, they can conclude that they must have green eyes, and then leave on the second.
Suppose there were 3 people. If I see two people with green eyes, I'll wait to see if they'll leave on the second night. If they do, then I know I have blue eyes; otherwise I know I have green eyes. Thus we all leave on the third night.
Repeat to get that everyone leaves on the 100th night.
Rockets don't go straight up. Why not?
Unless they went really far, they'd just fall back down. So instead they curve sideways, to then orbit the planet. It's like falling, but while moving sideways fast enough that the ground curves away from you before you can hit the ground, forever. This is called a gravity turn.
Suppose Alice and Bob are fruit growers. Alice is slow at making apples, and mediocre speed at making oranges. Bob is fast at making oranges, and really super duper extra fast at making apples.
Despite Bob being better at everything than Alice, they can trade to both be better off. How come?
Bob's time is best spent making apples - every orange made uses up time that could've been spent making even more apples. Alice's time is best spent on oranges. They should specialize in what they are best at, then trade to get whatever of the other fruit they need, so both will have more of each fruit. This is known as the law of comparative advantage.
Say I'm buying insurance. The insurance company charges a price that'll make them a profit on average, given however much risk I have of triggering a payout. So I must be losing money, on average.
How come I still might want to buy insurance, then? Is one of us necessarily being scammed?
An extra dollar is worth less to you the richer you are, so losing a dollar hurts more than gaining one. Approximately speaking the extra amount that losing hurts is worse when you are poorer than when you are richer - it's a greater fraction of your total wealth.
Therefore, poorer people are hurt more by risks than richer people. A 10% chance of losing $50k is much worse than a guarantee of paying $5k if I'm a normal person, but is not that different if I'm a billionaire. A richer person can thus profit on average by selling me insurance, while I am happy to have less risk.
Additionally, a big company can sell insurance to lots of people, and thus exploit averages to reduce their risk.
If I flip a coin and get 9 heads in a row, what's the chance the next flip is tails?
50%. Beware the gambler's fallacy - the coin doesn't have memory!
Suppose someone takes a mammogram (a breast cancer test). If they have cancer, it'll detect it most of the time (90%). If they don't, it'll still say they have cancer 10% of the time.
Among 40 year old women, 1 in 1000 have cancer. If a 40 year old woman gets a positive result on her mammogram (as in, it says she has cancer), what probability does she have cancer?
About 1%: the prior is around 1:1000 odds of cancer. If she has cancer it'll say so 90% of the time, but if she doesn't it'll still say so 10% of the time, so each cancer case becomes 90 positive results and each healthy case becomes 10k positive results, giving us final odds of 90:10k ≈ 100:10k = 1:100 ≈ 1%. Having cancer is so unlikely that the test isn't enough evidence to make you think you likely have cancer.
20
One can, on demand, produce quick sketches of islands and bridges to make puzzles like the Bridges of Konigsberg - then either challenge them to solve different sets of bridges, to draw their own for you to solve, or (perhaps for older kids) to figure out how their uncle can tell at a glance which puzzles will be possible.
Or if you play with the rule that you can add or remove one bridge before you start, then it should always be solvable, which might be more impressive than "This one is unsolvable, trust me"
10
There's one that's hard to guess, but easy to test if you have a small pool or even a kitchen sink (from Aha! by Martin Gardner).
In a pool there's a boat with heavy gold in it. You throw the gold at the bottom of the pool. Of course, the boat rises, but what about the level of the water in the pool?
I love asking children (and adults in some cases) the following question:
Five birds are sitting in a tree. A hunter takes a rifle and shoots one of them. How many birds are left?(Edit: Rephrased to avoid several problems)Five ducks are sitting in a field. A hunter shoots and kills one of the ducks. How many ducks remain sitting in the field? (If your answer is 'four' - try again!)
This is a system I/system II trap, akin to "which weighs more, a pound of feathers or a pound of gold?" In my experience kids (and adults) usually get this wrong the first time, but kids get a special kick out of something that sounds like a math problem they do for homework but turns out to be a bit more. I've also used the 2, 4, 8 puzzle for impromptu demos of confirmation bias. These are fun and engaging ways to teach kids about cognitive biases before they could realistically read the Sequences or Thinking Fast and Slow.
Can we share or brainstorm any more? Some basic inclusion criteria (feel free to argue or suggest more):
I don't have any kids of my own but have local friends with younger families. Having a few tricks like these really helps me create a "fun uncle" persona, but I'm also curious if parents have a different perspective or experience posing these kinds of questions to their kids.