[unreality]

I made up a magic trick today, it's a good one Very hard to spot the numerical property that makes it work if you're being presented to, though typing it out here will probably mean you will spot it instantly

basically, in it's not-spiced-up level it goes something like this:

* roll two dice

* find the sum of the two numbers

* find the difference of the two numbers

* add together those two values (the sum and the difference of the numbers)

* take this number and multiply it by the lower number squared

* say the result

from the result alone, I can determine the values of both dice! How?

Chop off the last two bullet points, and have the person speak that result- from that number I could glean the value of the highest die, but not the lowest. I need the next step to figure out the lowest

[Guest]

Well, if the numbers are x and y, then the sum of both the sum and difference of x and y:

(x+y)+(x-y)=2x

So the final answer would be 2xy^2, not exactly sure how you determine the numbers from that.

[Yoruichi-san]

Haha...nice ...yeah, when they have these on those TV magic shows I always figure out the trick instead of actually doing it...

Well, at least *you* spend your time thinking about new magic tricks...*me*, I spend my time thinking up new ways of killing people while having an airtight alibi...;P

[HoustonHokie]

Well, if the numbers are x and y, then the sum of both the sum and difference of x and y:

(x+y)+(x-y)=2x

So the final answer would be 2xy^2, not exactly sure how you determine the numbers from that.

you hit right on it with the answer to the first part being 2x. That's how you know what the upper number is - you divide what the person says by two. Now, what you need is the lower number. It happens that there are only 21 possible answers to 2xy^2, and they are all unique. If they're unique, you know the high and low roll.

[Guest]

Giving you the number I calculated, follow your instruction, then you will

Devide it by 2 and let say get value A after devided by 2

if A is cube number, 1, 8, 27, 64, 125, 216,

then there are (1,1), (2,2), (3,3), (4,4), (5,5) or (6,6) respectively

if not, and A is less or equals to 6, then is (1, A)

if not, and A can be divided by 4 but not 16, then is (2, A/4)

if not, but A can be divided by 9, then is (3, A/9)

if not, but A can be divided by 16, then is (4, A/16)

if not, but A can be divided by 25, then is (5, A/25)

if not, I actually give you numbers from somewhere else

[bonanova]

If a and b are the dice values, he speaks 2ab².

Suppose he speaks 100.

Divide by 2 - get ab² = 50 - not a cube, so a and b are different.

divide 50 by 1 2 3 4 5 6 and look for squares: 50 25 non-integer non-integer 10 non-integer.

25 is a square: ab² = 2 x 5². a=2 b=5.

[Prime]

I made up a magic trick today, it's a good one Very hard to spot the numerical property that makes it work if you're being presented to, though typing it out here will probably mean you will spot it instantly

basically, in it's not-spiced-up level it goes something like this:

* roll two dice

* find the sum of the two numbers

* find the difference of the two numbers

* add together those two values (the sum and the difference of the numbers)

* take this number and multiply it by the lower number squared

* say the result

from the result alone, I can determine the values of both dice! How?

Chop off the last two bullet points, and have the person speak that result- from that number I could glean the value of the highest die, but not the lowest. I need the next step to figure out the lowest

When you directed to find the difference of the two numbers, you forgot to specify to subtract smaller from larger. Without that stipulation your formula only guarantees to determine the lower number every time.

Edited August 5, 2008 by Prime

[unreality]

the difference between them will always be the absolute value difference, ie, the higher minus the lower

yeah this is how I stumbled across the idea:

I was playing around with two dice, until I realized that when you add the sum to the difference, it can never be odd! It has to be even... so I figured that out in my head and then later thought about after a few things (I was always getting double) and realized that it was always double the first number! The sum of the two plus the number that makes the lower number higher to equal the higher number will always be 2x where x is the higher number. ie x+y+x-y = 2x+y-y or just 2x. So I was like "wow, that's not easy to initially spot, that could make a great magic trick". Then I thought it would be kinda lame to guess just the top number (which I could do by dividing by 2, voila) so I tried to figure out a way to get the lower one too... one thing I sort of settled on was multiplying it by the lower number... but then say the result is 24- divide by 2 to get 12. Is that 6,2 or 4,3? etc

So then I came up with squaring the lower number. Now you have to figure out what square goes in.

ie, if the person says 90, divide by two to get 45. Which squares go into 45? 1 and 45- but there's no 45 on a six-sided dice. 16,25,and higher don't. The only that fits is 9. 9*5 is 45. So the dice are 5 and 3 (the sqr root of 9)

[Guest]

mmm Maths!

[unreality]

haha ;D