Old Old AMC 8 problem

MathIsGreat · P versus NP Offline Joined: 20 Jan 2008 Posts: 32

I saw this from an old AMC/AJHSME contest from 1998:

A 4x4x4 cubical box contains 64 small identical cubes that exactly fill the box. How many of these small cubes touch a side or the bottom of the box?

A)48 B)52 C)60 D)64 E)80

HELP PLEASE AND EXPLAIN

I tried so many times but I can't get it... Wallbash Red

**Posted:** Tue Nov 03, 2009 8:44 pm

mavropnevma

B) $52$ . All $16$ cubes of the lowest tier, and the $12$ cubes each on the contour of the other three tiers.

**Posted:** Tue Nov 03, 2009 10:57 pm

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randomguy64

Let's use complementary counting.

The cubes not touching a side/bottom of the box is 2x2x3=12; so, there are 64-12=52 cubes that do, as previously gotten.

**Posted:** Wed Nov 04, 2009 6:17 pm