Mathematicians have just created three new operation symbols, @, $,and _, each doing a different thing to a pair of numbers (All of these symbols can be derived from already-known operations and notations). The following equations using the new symbols are correct:

5@5= 2/5
2@2= 1
2@3= 5/9
3@4= 7/16
2@4= 3/8

1$0= undefined
1$4= 1/10
4$1= 1/10
10$10= 1/50
(1@1) $ 1= (√2)/10

2_2= 6
2_3= 9
6_2= 42
3_5= 30
5_6= 90

If the previous equations are correct, compute the following equation.

1 @ (1 $ (1_1))=

a $ b = 1/(5*sqrt(a*b))  if  a @ b = (a+b)/b*b.  Thus if also a _ b = b*a*(a+1)/2 we have 1 @ (1 $ (1 _ 1)) = 30. Thanks to Brian Smith and TomM for their contributions.

Posted by Richard on 2004-03-31 16:40:37