Miss Honey and Miss Wormwood were taking their classes out on an outing. The two classes were of different sizes, but in each class there were the same number of girls as boys.

Miss Honey told the children in her class to form pairs, each consisting of a boy and a girl. For her own amusement, mentally calculated the number of different ways this could be done.

Miss Wormwood also told her class to form into pairs, but with at least one single-sex pair. She also insisted that the girls Matilda and Susie did not pair up together as they were the most troublesome of her girls. She too calculated the number of different ways that this could be done.

Both teachers arrived at the same answer. How many children were in each class?

(In reply to need a better formula by Bob Smith)

http://mathworld.wolfram.com/DoubleFactorial.html

For Ms. Honey I agree with H(n)=(n/2)!

For Ms. Wormwood my formula is W(n)= (n-1)!! - (n-3)!! - (n/2)! which can also be written (n-2)(n-3)!! - (n/2)!

We reach the same conclusion:

H(12) = 6*5*4*3*2*1 = 720

W(10) = 9*7*5*3*1 - 7*5*3*1 - 5*4*3*2*1 = 720

 

 

Posted by Jer on 2005-09-22 19:17:57