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new operations (Posted on 2004-03-31) Difficulty: 3 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Thank you | Comment 10 of 14 |
I enjoyed the problem, Victor, and was able to resolve it without reading the postings (I'm the type that will fail to solve something for days rather than look at the solution, if I think the problem was well stated, as was the case here!).  I rated it a 4 because it was fun to solve, but I am new here and am leary of issuing a 5 before I've got a better grip on how I should rate things.

I will offer this problem to the University of Houston Math Enthusiasts, a happy group that will be happier for having had the opportunity to work on your question.

Robert

  Posted by Robert Mendez on 2004-04-01 03:29:50
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