EroticOrogeny
Upthrust
- Joined
- Jan 10, 2009
- Posts
- 2,266
What regifting thing?
From a little while back in this thread - your question:
Don't know if I am allowed to put this on here but I sure would like to know how it's done!
How does this work??!!
and my response:
Yes, basically. The answer is always a multiple of 9:
a = 10*n + m - n - m,
where n and m are integers between 0 and 9 (i.e., a digit).
The first page always seems to start with 25 - 2 - 5 = 18,
so there n = 2 and m = 5.
We can continue our algebraic manipulations:
a = 10*n -n = 9*n
Each multiple of 9 box is filled in with the same item, the other boxes don't matter. The only thing I don't know is how the boxes are filled for each cycle - is it a random number or a simple loop over names.
Similar to the problem of squaring a number ending in 5,
for example,
35 * 35 = ?
The shortcut gives 3*4 = 12, and add a 25 on the end:
35 * 35 = 1225
This holds for all positive integers, thus
for 55 * 55
we have 5*6=30, and the answer is 3025.
This was a little problem posed in Martin Gardner's Mathematical Games in Scientific American a long time ago.
For extra credit, find the rule for cases where the sum of the final digits is 10
(e.g., 33*37) and show that this is true.