Odd and even?

Originally posted by howardbradley
Is the rule this: how many times can n be divided by 2 before a fractional result is produced?

Put another way, what is the power of 2 in the (unique) factorization of n.

e.g. 56 = 2^3 x 7 - the power of 2 is odd
100 = 2^2 x 5^2 - power of 2 is even
11235840 = 2^9 x 3 x 5 x 7 x 11 x 19 - power of 2 is odd

Originally posted by howardbradley
Is the rule this: how many times can n be divided by 2 before a fractional result is produced?

Put another way, what is the power of 2 in the (unique) factorization of n.

e.g. 56 = 2^3 x 7 - the power of 2 is odd
100 = 2^2 x 5^2 - power of 2 is even
11235840 = 2^9 x 3 x 5 x 7 x 11 x 19 - power of 2 is odd

Originally posted by iamatiger
That's what I thought too - the operation mentioned in the question where two elements of the same type combine to make even, and two elements of different types combine to make odd, is multiplication.

The rule is whether the number of letter is the spelling of the number is odd or even. For example, 2 is spelt "two", which has 3 letters, 3 is odd, so 2 is odd.

Now why doesn't Red Hot Pawn let people key or select from a pop-up list how often they're prepared to move when they invite someone for a game. I could be offering to move every 5 minutes, someone who is prapred to do the same could accept the invitation and I could be doing what I cam here for ... playing chess !

uChess link at the bottom of the page...sadly is mostly empty when i go...but if more people knew about it....

Ah, i was thinking along the lines of the sum of prime divisors and later the sum of the primepowers 🙂

Originally posted by STANG
The rule is whether the number of letter is the spelling of the number is odd or even. For example, 2 is spelt "two", which has 3 letters, 3 is odd, so 2 is odd.

Now why doesn't Red Hot Pawn let people key or select from a pop-up list how often they're prepared to move when they invite someone for a game. I could be offering to move every 5 minutes, som ...[text shortened]... e same could accept the invitation and I could be doing what I cam here for ... playing chess !

Originally posted by Acolyte
Indeed. The next set is the set of patterns that can be made by colouring in an even number of squares on an infinite grid, like this (the 8s represent coloured squares):

888
080
080 is ODD
080

800
080 is EVEN
808

Originally posted by iamatiger
Hmm, is there still some operation that combines odd & even to make odd and otherwise makes even?

No takers? I assure you that this is a parity property. The property should be familiar to those who've seen the following puzzle:

'Take a chessboard, and cover two diagonally opposite corners with coins. Can you cover the rest of the board with dominoes (which occupy two squares on the chessboard)?'

Bump (for the benefit of royalchicken)

Originally posted by howardbradley

Put another way, what is the power of 2 in the (unique) factorization of n.

Originally posted by Acolyte
No takers? I assure you that this is a parity property. The property should be familiar to those who've seen the following puzzle:

'Take a chessboard, and cover two diagonally opposite corners with coins. Can you cover the rest of the board with dominoes (which occupy two squares on the chessboard)?'

Not quite. As I have said, the property I'm using is a parity property, so there has to be some way of combining the patterns that preserves total parity. You've got the parity of your examples correct, except that

0880
8008 is EVEN
0088

Originally posted by Acolyte
Not quite. As I have said, the property I'm using is a parity property, so there has to be some way of combining the patterns that preserves total parity. You've got the parity of your examples correct, except that

0880
8008 is EVEN
0088