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3 interesting/fun word problems from TFA:

1) A bat and a ball cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost? ____cents

2) If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets? ____minutes

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? ____days

How did you do? (see article for answers)



Got all three, but I'm a massive outlier on these things (statistician and developer, with a keen interest in physics), so they're questions that match patterns for the "you need to think about this" trigger in my head.

I find I fall over far more on things that hit that trigger needlessly, rather than the other way around (problems that look like I need to think about, but where the intuitive result is the correct one).

All things considered, I'd rather have the problem that way around and over-think and lose time needlessly than get the wrong answer more often. However, I'm biased to wanting that to be the best way, so I'm unreliable as to saying to what degree it's a "better" way to think.


I have to wonder if #3 isn't a quick thinking/pattern match for people with a CS background. Instant trigger/right for me. I'd think that people who work algorithmically should do better than a control group. I'm defensive with that statement because there's quite a few "people studying the subject do no better than the average" experiments (in economic) but I think there's a difference between academic knowledge and applied knowledge so if you think about complexity problems often you should do better on this one.

The interesting takeaway for me is that environment probably matters. If I take a test like this in a very relaxed environment I'm probably slowing down automatically.


All three of them were a pattern match for me. The first one was an obvious "Subtract the difference, split the remainder" problem. The second one I immediately thought "What's the rate?", did a little math, and figured out that in both cases one machine builds one widget, so it'll still be 5 min/widget. The third one is a classic exponential growth problem.


I suspect that they are a lot easier when you are primed with the idea that they are trick questions.


Probably yes, but the point is that if you've seen similar problems before, the fact that they are counterintuitive trick questions is part of your pattern-match, and so you jump to a problem-solving strategy that manipulates the data you're provided in a way that's accurate rather than one that's not.

It's the same way you build expertise in any domain: proceed with your initial hypothesis, but then once experience proves you wrong, build a new, more accurate mental model. That new model will give right answers in a greater percentage of cases, but inevitably it's wrong too, and so you repeat the process.


Agree about #3. On reading "doubles" my brain went "2^x" by reflex.


Those were fun.

I quickly came up with the incorrect answers for #1 and #2, but was able to realize that something was wrong with them and thought about it for a few more seconds and got the right answers.

I had the right answer with "fast" thinking for #3 though.

Note: When I say quickly & fast, I mean in less than a second, just the impulse answer. That is what fast thinking is I believe, but correct me if I am wrong.


These fast thinking problems rely on pattern recognition, so they will be easy if you have already seen the pattern, but you will fail if you apply the wrong pattern. Problem 3 tricks people who are used to everything being linear, which would probably be rather few people on HN.

I think the important skill is to be on the lookout, in your fast thinking, for problems which are slightly off. This is a clue that the pattern doesn't fit, and you should revert to slow thinking.


Am I the only one that got tripped up by the wording of the second question? My immediate thought was, "Does that mean five minutes EACH or five minutes TOTAL?"

Without a clear question, my brain refused to give an answer, so I got it wrong. It annoys me that it is presented without enough information and then you're told, "Your intuition is not as good as you think it is."

1 and 3 were fun though.


Interesting and fun? Not for me; all three are decades old and very well-known (the answer to the first jumped out the moment I read $1.10, possibly earlier; for the third, I scanned ahead to the 48). I would think any 10 year old with a knack for puzzles would know of these. If not, kids surely have changed over time. Maybe those PCs and iPads provide superior distractions?


1. The impulse to say 10 cents was there, but solving the equation led to the right answer.

2. Got this right in a few moments by thinking about it (no math).

3. Instantly knew the answer thanks to having watched "the most important video you'll ever see": https://www.youtube.com/watch?v=F-QA2rkpBSY




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