Odd and even?

This game works as follows: by some mathematical rule, I will assign 'odd' or 'even' to all elements of a set. Two elements combined in some way will give even if they are of the same type, and odd if they are not. The object is to guess the rule, by asking whether specific elements are odd or even.

The first set is the natural numbers (ie 1,2,3,4,5,6....)

24 is ODD
100 is EVEN

Originally posted by Acolyte
This game works as follows: by some mathematical rule, I will assign 'odd' or 'even' to all elements of a set. Two elements combined in some way will give even if they are of the same type, and odd if they are not. The object is to guess the rule, by asking whether specific elements are odd or even.

The first set is the natural numbers (ie 1,2,3,4,5,6....)

24 is ODD
100 is EVEN

Originally posted by royalchicken
Is 64 odd or even?

How about 32?

I would like to know the parity of the following numbers;

2, 4, 5, 10 and 15. I already have an idea what the rule might be, i'm hoping for EEOOE

2 is ODD
4 is EVEN
5 is EVEN
10 is ODD
15 is EVEN
32 is ODD

Master37: If your rule is what I think it is, you're on the right track; it may in fact only be one word out.

How's that for a confusing clue?

Hmmz....the 5 being even disrupts all my theories...how about 7, 11 and 12?

7 is EVEN
11 is EVEN
12 is EVEN

I need building blocks..

How about 1,3,8 and 81?

1 is EVEN
3 is EVEN
8 is ODD
81 is EVEN

I can see this bugging me! Okay, so so far we have

Even :
1 3 4 5 7 11 12 15 64 81 and 100.

Odd :
2 8 10 24 32

All of the "odd" numbers are even and all square numbers suggested so far are "even".

2x32=64 is also the product of two "odd" numbers which gives an "even" result. Hmmm....

And square numbers are the products of two numbers of the same type.. I'm feeling good about this one!

Let's test...

6 and 56, are they both odd?

For completeness sake, how about 9 and 6?

is 11235840 odd?

6 is ODD
9 is EVEN
56 is ODD
11235840 is ODD

Sound's like you're on to something, mikenay. iamatiger, I'd be intrigued to see the significance of your number.

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