Well, they can know the number, but not how fast you are thinking it.
Well.... If they know how fast, they might be able to know the number :-)
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Think of a Number. How Do Math Magicians Know What It Is?
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Re: Think of a Number. How Do Math Magicians Know What It Is?
#22Earlier quoted context omitted.
Since Peter is given the product of the two numbers, he should instantly know the pair if both numbers are prime, but since he doesn't it rules out pairs like (7x11) = 77 and (2x53) = 106. Sandy knows the sum and has now been told that Peter doesn't know the pair. If the sum had been 6, the following pairs are possible: (1+5) (3+3) (4+2), Peter has just ruled out (1x5) and (3x3), so Sandy would be able to narrow it d…
>since he doesn't it rules out pairs like (7x11) = 77 and (2x53) = 106. I think pair (7x11)=77 can't be rule out, because pair (1x77) is also equal 77. still don't got it... Can you explain the situation for 3 turns before Peter knows, Sincere thanks.
Probably easier if you imagine it with a much smaller range of numbers, like 1-9, or even 1-3
Re: Think of a Number. How Do Math Magicians Know What It Is?
#23Earlier quoted context omitted.
Since Peter is given the product of the two numbers, he should instantly know the pair if both numbers are prime, but since he doesn't it rules out pairs like (7x11) = 77 and (2x53) = 106. Sandy knows the sum and has now been told that Peter doesn't know the pair. If the sum had been 6, the following pairs are possible: (1+5) (3+3) (4+2), Peter has just ruled out (1x5) and (3x3), so Sandy would be able to narrow it d…
>he should instantly know the pair if both numbers are prime That should actually be "if the product of their respective smallest prime factors is over 100". 7x11 can't be ruled out since 1x77 also produces 77, whereas 49x17 and Nx53 can be ruled out. You can also rule out some of the larger squares, e.g. 25x25 and 64x64, so there's probably still a better phrasing for that Edit: Can also rule out 1xPrime
Oh whoops, good pickup; I'd like to say I tried to simplify it for the explanation and brevity, but I completely overloooked that 1xn = n.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#24Then there's the time with David Blaine and George W. Bush:
Re: Think of a Number. How Do Math Magicians Know What It Is?
#25Hey this doesn't mention the simplest trick of all: get them to do a bunch of useless operations, then multiply by 3, add all the digits, and you'll know the final number.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#26Reminds 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'…
CVE-2022-123456: The specification doesn't require each new round to be dependent on the input from the previous round. This can allow unprivileged users to send arbitrary commands to the accelerator and breaking system.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#27Unless I'm misunderstanding, I think problem 3 has many solutions.
Spoilers:
First note that, below 16, 11 is the only sum which explains S's first statement: all possible pairs of numbers adding to 11 have non-unique products, accounting for S knowing P would not know the numbers.
Then note that for 18 (9x2), 24 (8x3), and 28 (7x4), all other factor pairs for that product add to a non-11 number below 16. Those non-11 sums are ruled out by S's first statement, so P will know the sum is 11 by her second statement.
Therefore (9,2), (8,3), and (7,4) all look like valid solutions, and it seems likely there are more.
What am I missing?
Re: Think of a Number. How Do Math Magicians Know What It Is?
#28Earlier quoted context omitted.
Yeah, I read this explanation, and I'm probably being very dense, but I still don't get it :)
Tip: A simpler variant of essentially the same puzzle principle is the xkcd "Blue Eyes" puzzle. https://xkcd.com/blue_eyes.html
Love this! Took a while to find the solution :)
Re: Think of a Number. How Do Math Magicians Know What It Is?
#29It's arithmetic, at most.
Re: Think of a Number. How Do Math Magicians Know What It Is?
#30I've been working on something related for fair salary negotiations, where the two parties think of their honest salary proposal, exchange random numbers and exponents with each other, perform some arithmetic using the random number and their own secret honest salary number, and then decide whether the result is acceptable to both. I started hacking on this protocol using a pencil and paper variation of Diffie-Hellma…
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