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Good brainteasers for children?

by ejacob1 min read2nd Mar 202112 comments

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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):

  1. Problems/tasks should reliably trigger some cognitive bias or other "glitch."
  2. Any stepwise thinking needs to be finished within a child's attention span. Feel free to assume it's a particularly smart and motivated child if you need to.

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.

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5 Answers

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?

Nice one! Took me a moment :)

You can use the questions from the Cognitive Reflection Test

  1. 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?
  2. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
  3. 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.

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!

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"

Good suggestion, and the username checks out.

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?

5 comments, sorted by Highlighting new comments since Today at 8:10 PM

Five birds are sitting in a tree. A hunter takes a rifle and shoots one of them. How many birds are left? (If your answer is 'four' - try again!)

0 cause the other 4 all fly off? (my guess)

5 because even though the bird was shot it is still on the tree?

1 because both are true?

(I did immediately thought 4 and only thought about it more after you said it was the wrong answer)

Yes, 0 because of the noise.

Yeah: "are left" has an ambiguous definition. Also, too, what hunter is using a rifle to shoot birds that sit in a tree? Every kind of tree sitting bird I know of is either endangered or a songbird. And hunters typically use a shotgun with birds hot to hunt duck or quail or what have you, not a rifle. The whole thing doesn't actually work, once given some thought. Especially as the "trick" relies on experience with birds that an urban child may not even have.

These are all true, but not things that children know or worry about. You are right that it does require some natural experience with birds being skittish around noises or other stimuli.

A better version might be: Five ducks are sitting in a field. A hunter shoots and kills one of the ducks. How many ducks remain sitting in the field?

Or, if you want the answer to be 1 instead of 0 and to be slightly less helpful, "how many ducks remain in the field?". (The specificity of "sitting" may give a hint that a bit of careful thought is called for.)