- 01 Jun '04 21:22This 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 - 01 Jun '04 23:06

Is 64 odd or 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 - 03 Jun '04 14:32I 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? - 03 Jun '04 23:54Is 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