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))=

(In reply to And $ Makes 30 by Richard)

30?

1_1=1
1$1=1/5
1@(1/5)=(6/5)/(1/5)=6

Where did you or I go wrong?

Edit:  Yes, I went wrong...
The last line should equal (6/5)/(1/25)=30

Edited on April 1, 2004, 4:06 am

Posted by Tristan on 2004-03-31 18:33:18