 Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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 February 10, 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 solutionss.

Problems in Mathematics of KöMaL, January 2009