Stormy:
FOGREACASST= capital gains forecast
That is clever, I never thought of the Caps.
I am a three digit number!
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I? 194
N^3 + 2N
Consider, for simplicity, a 3 digit number 'abc", such as 321.
Suppose that a+b+c is divisible by 3.
Our number, written as 'abc' is actually 100a+10b+c.
For instance, 321 = 100*3+10*2+1.
Let's rewrite 100a+10b+c as 99a+a + 9b+b + c.
99a+a + 9b+b + c = (99a + 9b) + (a + b + c)
The first part is always divisible by 3 since numbers with all nines are always divisible by 3 (9 = 3*3, 99=33*3, 999=333*3 etc).
That the second part (a+b+c) is divisible by 3, is a given.
So, we have a sum of two parts, both of which are divisible by 3. This sum is, therefore, also divisible by three.
Theorem proven.
HOW MANY SQUARES ARE THERE?
Even though I know what I meant, I should have made this clearer by adding:
Board Size 10x10, made up from 100 1x1 squares. Ok! So there are 100 little squares on the board; how many squares are there
GLOOOOKGD
CDILSCUODUNETD
(just kidding)
