Pick any four digit number, not all of the digits the same. Write the digits in descending order, and write the digits in ascending order, and subtract the larger from the smaller. For example:
Pick 6436
6643 - 3466 = 3177
Now do the same thing with the new number.
Do this a total of seven times (if at any time you get a three digit number, treat it as a four digit number; i.e, if you get 738, think of it as 0738, and your new number is 8730 - 0378 = 8352).
Concentrate on your final number. I’m now gonna strain all my powers of concentration to read your mind across the internet:
4[sup]3[/sup]-3[sup]3[/sup]+2[sup]3[/sup]-1[sup]3[/sup]=44, which, by an eerie coincidence, is my apartment number.
[sub]The area of a circle with radius R is…?[/sub]
Given that Q is a whole positive number and is the product of X and Y, where X+1=Y, X[sup]2[/sup] + X - Q = 0. The absolute values of the roots of that function give {X, Y}.
Right now I’m working on one to give the circumference and area of a standard n-gon given the length of its longest diagonal A. If someone else wants to, feel free.
Write down ‘12345679’ (no 8, notice) on a piece of paper.
What number did you think was the hardest to write?
1? Multiply the above by 9.
2? “” “” 18.
3? 27.
4? 36.
5? 45.
6? 54.
7? 63.
9? 81.
(8 and 72 works also…)
Solve: (x-a)(x-b)(x-c)(x-d)…(x-z) = ?
November 29, 1999 was the last day with all odd digits for just over 1000 years.
Feb 2, 2000 was the first day with all even digits since September 28, 888. (IIRC…)
Yeah, some numbers will get there quicker than others; I said do it seven times because, depending on what number you pick, it may take as many as seven steps to get to 6174. 6174 is called “Kaprekar’s constant”, Kaprekar was an Indian mathematician credited with discovering that.
Here’s something else (it’s a very famous one, I’m sure many of you have seen it before):
Pick any positive integer.
If it’s even, divide it by 2.
If it’s odd, multiply it by 3, then add 1.
Repeat for the new number, and continue repeating indefinitely.
For example, start with 17:
17…52…26…13…40…20…10…5…16…8…4…2…1
Whatever number you pick, it seems you will always eventually end up at 1 (it’s been tested for all numbers with 15 digits or less, and they all work). Thing is, no one has ever proved that; it’s a really hard problem. Anyone who could prove it would definitely get a lot of recognition, and a nice bit of cash to boot.
(It’s known by many names–The Syracuse problem, the Hailstone problem, the 3n+1 Problem, the Collatz problem, to name a few).
Five hundred twenty-five thousand, six hundred minutes
Five hundred twenty-five thousand moments so dear
Five hundred twenty-five thousand, six hundred minutes
How do you measure, measure a year?
In daylights? In sunsets?
In midnights? In cups of coffee?
In inches? In miles?
In laughter and strife?
In five hundred twenty-five thousand, six hundred minutes?
How about love?
After fuddling around with these numbers for a few hours today (and having to take a nap partly because of that), I have come up with the following nearly useless math stuff:
Given that X is the length of the longest diagonal possible in a regular n-gon (all sides equal length, all angles equal size), N is the number of sides in the n-gon, and Y is the smaller angle created when the diagonal is drawn:
Y N
45 4
40 5
60 6
51.4 7
67.5 8
1/2 sin Y = length of side Z of an n-gon as described above.
ZN=circumference of n-gon.
Z* cos(((N(180N-360))-90)=A. Y[sup]2[/sup]-A[sup]2[/sup]=B[sup]2[/sup]. 2(BA+AY)=area of the . . . well, hexagon.
Later today I’ll work on one for hectagons and octagons. There has to be some sort of universal way of figuring this shit out.
