Lesson 4: Dividing a number of runes between two people 
[Aug. 1st, 200606:21 pm]
Arithmancy: HP math geeks unite

There is some overlap between different magical subjects, of course, and Arithmancy can often be useful in other subjects studied. If you have taken Ancient Runes above the OWL level, for example, you may have been taught this particular spell for dividing a set of runes between two people in such a way as to ensure that each of them is dealt the predetermined number necessary for a reading. (As you may be aware, some people cheat when using runes in order to manipulate events to their liking. Experts in reading runes have long employed Arithmancy to prevent this from happening.) For safety’s sake, in this lesson we will practice with Everyflavour beans instead of runes.
The Spell
 Ask person 1 to take between 10 and twenty beans, but not to tell you how many they took.
 Have person 2 count the number of beans person one took, and then to take twice that many.
 Tell person 1 to give a certain number of her beans to person 2 (any single digit number, for example, 3, 4, or 5).
 Person 2 will then again count how many beans person 1 has and give her twice that number from her own.
You now know exactly how many beans Person 2 is holding: three times the number you gave in step three.
Why does this work? A little Muggle algebra provides all the magic we need.
Suppose person 1 takes N beans. Then person 2 will have 2N beans, so there are a total of 3N beans to work with.
Now you tell person 1 to give M beans to person 2, and so person 1 will have N  M beans, while person 2 has 2N + M beans.
Finally, person 2 gives person 1 2(N  M) of her own beans. So let's think about how many beans each of them has at this point.
Person 1 has (N  M) + 2(N  M) beans, which simplifies to 3N  3M beans. Since we don't know what N was originally (person 1 chose it), we can't quickly see how many beans she has.
Person 2, however, has (2N + M)  2(N  M) beans, which simplifies to 3M beans! You chose the number M in step three, so you now know exactly how many beans person 2 is holding! 

