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
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.
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.
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):
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 !
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
Hmm, is there still some operation that combines odd & even to make odd and otherwise makes even?
Originally posted by iamatiger Hmm, is there still some operation that combines odd & even to make odd and otherwise makes even?
Yes, though you don't have to tell me the exact procedure, just the general idea.
888
808 is EVEN
888
88088
80008
80008 is EVEN
88088
8088
8000
0008 is EVEN
8808
I don't think it's giving too much away to point out that the position of the pattern on the lattice is irrelevant - you don't need to indicate where (0,0) is, in case you were wondering.
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)?'
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)?'
Well, for starters, opposite corners are the same color. Each domino covers one black and one white square, but after you've covered corners, you have 32 squares of one color and 30 of another, so you can't do the domino thang.
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
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
I'm not sure exactly how the combination rule works. Specifically, I don't know how any two odd sets can be combined to make an even one, but my interpretation of odd and even is obviously not quite correct. What about:
04 Jun '04 07:34
Odd and even?
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