Problem K. 198. (January 2009)
K. 198. The inhabitants of a certain planet use not four but five basic arithmetic operations. The operations of addition, multiplication, subtraction and division are the same as ours, but they also have a special operation denoted by the operation sign @. We do not know exactly how this operation works, but we have found out that the following properties are valid for all x and y:
(a) ,
(b) ,
(c) .
What is the value of on the planet in question?
(6 pont)
Deadline expired on 10 February 2009.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. A művelet tulajdonságait felhasználva:
12@5=5@12=(4@12)+12+1=3@12+2^{.}(12+1)=2@12+3^{.}(12+1)=1@12+4^{.}(12+1)=0@12+5^{.}(12+1)=12@0+5^{.}(12+1)=12+5^{.}(12+1)=77.
Statistics:
136 students sent a solution.  
6 points:  92 students. 
5 points:  11 students. 
4 points:  2 students. 
3 points:  3 students. 
1 point:  5 students. 
0 point:  15 students. 
Unfair, not evaluated:  8 solutions. 
