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 new operations (Posted on 2004-03-31)
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))=

 See The Solution Submitted by Victor Zapana Rating: 3.3000 (10 votes)

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 And \$ Makes 30 | Comment 6 of 14 |

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

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