Think of a Number. How Do Math Magicians Know What It Is?
quantamagazine.org
Think of a Number. How Do Math Magicians Know What It Is?
1–10 of 60 posts
Re: Think of a Number. How Do Math Magicians Know What It Is?
#2How about testing these puzzles on GPT3 or upcoming transformers?
Re: Think of a Number. How Do Math Magicians Know What It Is?
#3Reminds me of this problem:
Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers.
Then, this dialog occurs between Sandy and Peter:
Peter: I don't know the numbers.
Sandy: I don't know the numbers.
Peter: I don't know the numbers.
Sandy: I don't know the numbers.
Peter: I don't know the numbers.
Sandy: I don't know the numbers.
Peter: I don't know the numbers.
Sandy: I don't know the numbers.
Peter: I don't know the numbers.
Sandy: I don't know the numbers.
Peter: I don't know the numbers.
Sandy: I don't know the numbers.
Peter: I don't know the numbers.
Sandy: I don't know the numbers.
Peter: I do know the numbers.
What are the numbers?
Source: https://www.reddit.com/r/math/comments/32opae/next_level_che...
Re: Think of a Number. How Do Math Magicians Know What It Is?
#4My immediate reaction to "Think of a number...Magicians...": The tricks probably require that their targets think of only natural numbers - {1, 2, 3, 4, ...}. And assume that most folks will pick small, dull natural numbers. (Vs., say, 2^24-1. Which is the maximum unsigned mediumint value in MySQL. Or, if you've ever been stuck doing low-level stuff with a 80286 CPU...)
It'd be interesting to see if any of the tricks worked for, say, -7π + ei.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#5The Collatz Conjecture or the 3n+1 problem was mentioned last week https://news.ycombinator.com/item?id=31208035
Any positive integer you take, you end up in a 1-4-2-1 loop. It's not proved yet but there's no number found yet that satisfies otherwise.
Very interesting. What's the use case of this?
Impressing ladies at the bar with your 'deep connection'.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#6Reminds me of this problem: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don'…
No post body was provided.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#7Reminds me of this problem: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don'…
I still don't get it :D
Re: Think of a Number. How Do Math Magicians Know What It Is?
#8If it involves operations in steps, your “code” is manipulating the digits. Easy example. Suppose I ask you to think of a positive integer. Then I ask you to double it. Now, give me the last digit. It’s either zero, two, four, six or eight. With a few more steps I can probably get any number I like.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#9Reminds me of this problem: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don'…
I still don't get it :D
This comment from the linked Reddit thread explains how:
> Each sentence is extra data given to the other person.
> When Peter says "I don't know the numbers", means that he doesn't have enough information. For example, if the product of the numbers is 10, it could be (1,10) or (2,5). But if the product is 9801, then Peter would know the answer (99,99). Therefore, his first sentence reveals to Sandy that (99,99) isn't a possible answer. But even this extra data isn't enough for Sandy to know the answer, and she says so. Again, this is extra data for Peter, but , again, is not enough. This go back and forth until suddenly Peter gains enough information to find the answer.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#10Reminds me of this problem: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don't know the numbers. Peter: I don't know the numbers. Sandy: I don'…
A smaller variant if that puzzle is in the article.