Note: This must be done in your head only. Do NOT use paper and pencil or a calculator. Try it!
Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000 Now add 10.
What is the total?
I don't know why, but my answer was 5000, and it took me awhile to to figure out where I went wrong. Apparently 5000 is a very common mistake, so at least I'm not alone. (Although maybe that's not as much of a comfort as I thought...) Maybe it's like that trick sentence that actually uses the word "the" three times, but most people only count two. The brain automatically recognizes a pattern, and it extends that pattern into the future, even if it is incorrect to do so.
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18 comments:
I like these.
Another is when you tell someone you flipped a coin 50 times and it came up heads all 50 times, what's the probability the next flip will be heads?
People want to say a 100%, but it's still 1 out of 2.
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Any thoughts on Carlin? I know you loved him.
I got 5000 too. I added 10 to 4090 and got 5000 for some reason.
Mike - how is that a puzzle?? Basic statistics says that flip results are independent.
Stacey insisted it was 5000 as well. If you were to ask someone to do 1000 + 1000 + 1000 + 1000 + 40 + 30 + 20 + 10, I wonder if they would come up with 4100.
How is 4090+10 a puzzle?
I'm just saying it's a tricky wording that sometimes gets the mind.
Of course we all know the probability...just like we know 4090+10 is 4100.
I don't think I would have come up with 5000 if the question had been worded 1000+1000+1000+1000+40+30+20+10.
My feeling is that the wording of the question creates a sub-conscious pattern in the brain, and the correct answer of 4100 is at odds with the pattern answer of 5000.
I just think you need to slow down.
When you started this post with your "Note", I automatically went into "this-might-be-tricky-perhaps-I-should-go-slow" mode, and I got 4100.
Perhaps it has to do with our current culture. We're a fast, fast, fast, society not looking to spend too much time on any one thing, especially simple addition, so we look for shortcuts (like patterns) to solve the problem quicker.
But sometimes like I tell my students, you just gotta do the work.
I know in my classroom we spend a lot of time looking for patterns to help us solve problems, so kids are trained to look for them, and perhaps you both are just seeing the effects of a brain doing what it's been trained to do.
I definitely agree with you that slowing down would have helped, but it's hard for me to do. 1000+40 = 1040. 1040+1000 = 2040....etc, etc, etc, the answer is 5000. Oh shit, it's not!?
(And once I had 5000 in my head, it still took a few passes for me to find my error, even going more slowly)
I getcha. I showed the problem to a bunch of math teachers at this conference I went to today, and about half said 5,000.
I read that note and went slow too... and got 5000. So I did it again... and got 5000. I guess I'm not as smart as the math teacher.
I still insist the "probability of a coin flip" problem is not a puzzle.
I don't know if you can call the coin flipping probability a "puzzle," but most people are very confused about probability and statistics.
Like in basketball: if a 90% free throw shooter is at the line and has made his last 9 consecutive shots, if you asked most people the probability of the tenth shot going in, I'm willing to bet that most of them would not say 90%.
Exactly the same type of probability problem as my coin flip.
Again, Kevin's initial problem a puzzle??? To me it's straight addition.
And the coin flip problem is not a puzzle!!! Never said it was. Just said it was tricky.
WHERE DID THIS TALK OF PUZZLES EVEN COME FROM?!?!
So would you say that you are puzzle puzzled?
Haha, definitely.
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