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) $x \mathrel{@} 0 = x$ ,

(b) $x \mathrel{@} y = y \mathrel{@} x$ ,

What is the value of $12 \mathrel{@} 5$ 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

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.

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