MathDB

11

Part of 2005 AMC 10

Problems(2)

Not my favorite topic... CUBES

Source:

11/7/2005
A wooden cube n n units on a side is painted red on all six faces and then cut into n3 n^3 unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is n n? <spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 7 <span class='latex-bold'>(A)</span>\ 3\qquad <span class='latex-bold'>(B)</span>\ 4\qquad <span class='latex-bold'>(C)</span>\ 5\qquad <span class='latex-bold'>(D)</span>\ 6\qquad <span class='latex-bold'>(E)</span>\ 7
geometry3D geometry
Cubing digits sequence

Source:

11/17/2005
The first term of a sequence is 2005. Each succeeding term is the sum of the cubes of the digits of the previous terms. What is the 2005th term of the sequence? <spanclass=′latex−bold′>(A)</span> 29<spanclass=′latex−bold′>(B)</span> 55<spanclass=′latex−bold′>(C)</span> 85<spanclass=′latex−bold′>(D)</span> 133<spanclass=′latex−bold′>(E)</span> 250 <span class='latex-bold'>(A)</span>\ 29\qquad <span class='latex-bold'>(B)</span>\ 55\qquad <span class='latex-bold'>(C)</span>\ 85\qquad <span class='latex-bold'>(D)</span>\ 133\qquad <span class='latex-bold'>(E)</span>\ 250
modular arithmeticalgebraAMC 10recursionSequences