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K. 86. A large cube is put together out of small unit cubes. There are 80 small cubes altogether that lie along the edges or at the corners of the large one. How many small cubes does the large cube consist of?

(6 points)

This problem is for grade 9 students only.

Deadline expired on 10 October 2006.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás: A nagy kocka csúcsaiban 8 kiskocka van, tehát a nagy kocka éleinek közepén (nem számítva a két szélső kockát) összesen 72 kiskocka van. Mivel 12 él van, ezért egy él közepén 6 kiskocka van. Tehát a nagy kocka éle 8 kiskockát tartalmaz, így a nagy kocka 8.8.8=512 kiskockából áll.

Statistics on problem K. 86.
 342 students sent a solution. 6 points: 258 students. 5 points: 50 students. 4 points: 5 students. 3 points: 4 students. 2 points: 3 students. 1 point: 3 students. 0 point: 15 students. Unfair, not evaluated: 4 solutions.

• Problems in Mathematics of KöMaL, September 2006

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