This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.
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Math
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Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3
2×3
2^{34}
234
a_{i-1}
ai−1
\frac{2}{3}
32
\sqrt{2}
2
\sum_{i=1}^3
∑i=13
\sin \theta
sinθ
\boxed{123}
123
Comments
It's interesting how the vast majority are odd (19:7 ratio as of this moment, around 73% odd). This is statistically unusual considering that there is equal possibility for even and odd numbers to be made. I think I can explain this.
It is human nature to think that a number which is even is too rounded to be 'random', and since all even numbers are composite (trivial exception of 2), even numbers tend to be avoided.
Furthermore, chosing prime numbers is a popular trend when picking 'random' integers; we tend to think of numbers which are isolated. For example, prime numbers can be considered to be isolated, as it has no proper factors, hence there are no other numbers associated with it, as it were. Now, I understand prime numbers are not the most frequently generated 'random' numbers, but the fact that they are odd surely plays a part. This leads us to think odd numbers are more random than even numbers.
I guess this means that 'random' numbers generated by humans are not truly random.
Of course, this is only my speculation, based on my own experience. When I think of a random number, 37 comes to mind. I think the fact that both digits are odd, it's not too small or too big between 0 and 100, and it being prime leads me to believe it is the most random number. Ironically, if everyone thinks this way, it becomes one of the least random numbers.
Please feel free to post your opinions and speculations.
But there are people(like myself) who already have a predefined random number in mind. For example, if someone asks me to choose a number, I will always pick 4. This is just to avoid time spent in thinking of a random number. I know that this is not random, and the number of people who think this way are small, but yeah. Your observations make sense though.
Postscript: I was going to say that the folks that picked 0 like their coffee mocha, while those that picked 1 just want their coffee black. But, you're right, I read somewhere that when asked to pick a random number, 37 pops up much more frequently than expected, a fact that mind-trick magicians exploit. I picked 137 because that's the integer part of the reciprocal of the Fine Structure Constant. Does picking a famous constant at random qualify? I'm going to check and see how many of them are odd.
Haha :). I do not wish to get into the philosophy of the definition of 'random'. Although one short definition could include 'a choice without reason'. If an integer we chose truly was random, then there should have been absolutely no factors influencing our decision to chose it. Of course, that seems to be next to impossible.
It is a fact that humans suck at being random, even though they think it should be easy. Give anybody a marker pen and a whiteboard, and tell him/her to mark dots on the board at random. After it's "done", just about anybody can tell it isn't really random.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
**bold**
or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
...\]
to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
It's interesting how the vast majority are odd (19:7 ratio as of this moment, around 73% odd). This is statistically unusual considering that there is equal possibility for even and odd numbers to be made. I think I can explain this.
It is human nature to think that a number which is even is too rounded to be 'random', and since all even numbers are composite (trivial exception of 2), even numbers tend to be avoided.
Furthermore, chosing prime numbers is a popular trend when picking 'random' integers; we tend to think of numbers which are isolated. For example, prime numbers can be considered to be isolated, as it has no proper factors, hence there are no other numbers associated with it, as it were. Now, I understand prime numbers are not the most frequently generated 'random' numbers, but the fact that they are odd surely plays a part. This leads us to think odd numbers are more random than even numbers.
I guess this means that 'random' numbers generated by humans are not truly random.
Of course, this is only my speculation, based on my own experience. When I think of a random number, 37 comes to mind. I think the fact that both digits are odd, it's not too small or too big between 0 and 100, and it being prime leads me to believe it is the most random number. Ironically, if everyone thinks this way, it becomes one of the least random numbers.
Please feel free to post your opinions and speculations.
Log in to reply
But there are people(like myself) who already have a predefined random number in mind. For example, if someone asks me to choose a number, I will always pick 4. This is just to avoid time spent in thinking of a random number. I know that this is not random, and the number of people who think this way are small, but yeah. Your observations make sense though.
Hey your observation skill is awesome! @Jihoon Kang
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Thank you :)
Please see this note which is inspired by you.
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Postscript: I was going to say that the folks that picked 0 like their coffee mocha, while those that picked 1 just want their coffee black. But, you're right, I read somewhere that when asked to pick a random number, 37 pops up much more frequently than expected, a fact that mind-trick magicians exploit. I picked 137 because that's the integer part of the reciprocal of the Fine Structure Constant. Does picking a famous constant at random qualify? I'm going to check and see how many of them are odd.
Log in to reply
Haha :). I do not wish to get into the philosophy of the definition of 'random'. Although one short definition could include 'a choice without reason'. If an integer we chose truly was random, then there should have been absolutely no factors influencing our decision to chose it. Of course, that seems to be next to impossible.
Log in to reply
It is a fact that humans suck at being random, even though they think it should be easy. Give anybody a marker pen and a whiteboard, and tell him/her to mark dots on the board at random. After it's "done", just about anybody can tell it isn't really random.
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0, I just randomly thought of 2
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