Problem K. 104. (December 2006)

K. 104. We have a large supply of boxes: each of them is either small, or medium or large. 11 large boxes were put on the table. Some were left empty and 8 medium boxes were put in each of the rest of them. Some of the medium boxes were also left empty, and 8 small boxes (all empty) were put in each of the remaining ones. Thus there were 102 empty boxes on the table. How many boxes are there on the table altogether? (Boxes of the same size cannot be put into each other.)

(6 pont)

Deadline expired on January 10, 2007.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Amikor egy nagyobb dobozba 8 kisebbet teszünk, akkor az üres dobozok száma 7-tel nő, így ha először x, majd y dobozba teszünk 8 kisebbet, akkor az üres dobozok száma 11+x^.7+y^.7=102, ahonnan x+y=13, azaz 13^.8+11=115 doboz van összesen az asztalon.

Statistics:

144 students sent a solution.
6 points:	77 students.
5 points:	4 students.
4 points:	12 students.
3 points:	4 students.
2 points:	3 students.
1 point:	34 students.
0 point:	9 students.
Unfair, not evaluated:	1 solutions.

Problems in Mathematics of KöMaL, December 2006