Number of Cubies problem

[Igora]

I've been working out an equation for the number of cubies in a regular cube (not helicopter, skewb etc.) so far I've got c=6x^2-8x+4 where x is the number of cubies on one side of the cube, for instance in a 7x7x7 x=7. The only problem with this equation is that it doesn't work for a 1x1x1 cube. Any thoughts on one that would?

[brunson]

I don't think it works for 2, either.

Spoiler:

x^3 - (x-2)^3 works a bit better. That's how many blocks if the cube was solid, minus the number of cubies that would fit inside it if it were hollow.

(But it still doesn't work for 1)

[cmhardw]

I've been working out an equation for the number of cubies in a regular cube (not helicopter, skewb etc.) so far I've got c=6x^2-8x+4 where x is the number of cubies on one side of the cube, for instance in a 7x7x7 x=7. The only problem with this equation is that it doesn't work for a 1x1x1 cube. Any thoughts on one that would?

With x=3 your formula gives:
6*9 - 8*3 + 4 = 34

So it does not work for the 3x3x3 either.

Hint: You are on the right track, keep going with the corrections. For example, you know the 6*x^2 is an overcount, and counts more pieces than are actually on the cube. Take a look at your method for fixing this overcount (i.e. the other terms in your formula).

Chris

[JeffDelucia]

If I understand what your asking this should work

Spoiler:

c=x^3-(x-2)^3

[cmhardw]

If I understand what your asking this should work

Spoiler:

c=x^3-(x-2)^3

Yep Though usually people write the simplified form for this.

Chris

[JeffDelucia]

If I understand what your asking this should work

Spoiler:

c=x^3-(x-2)^3

Yep Though usually people write the simplified form for this.

Chris

1x1 doesn't work though...

[uberCuber]

If I understand what your asking this should work

Spoiler:

c=x^3-(x-2)^3

Yep Though usually people write the simplified form for this.

Chris

1x1 doesn't work though...

do you need a formula to tell you how many cubies are in a 1x1?? >_>

[cmhardw]

1x1 doesn't work though...

do you need a formula to tell you how many cubies are in a 1x1?? >_>

The 1x1x1 case fails on most formulas involving the n x n x n cube. Usually we just say that for the formula n > 1 must be true. It might be possible to come up with one single explicit formula that includes the 1 x 1 x 1 case correctly, but I don't know of one. That's not to say that it hasn't been done though.

Chris

[hawkmp4]

If I understand what your asking this should work

Spoiler:

c=x^3-(x-2)^3

Yep Though usually people write the simplified form for this.

Chris

1x1 doesn't work though...

do you need a formula to tell you how many cubies are in a 1x1?? >_>

No, but having an equation that works more generally is...well...nicer.

[Igora]

oops, I accidentaly posted the wrong one , the one I meant to post is c=6x^2-12x+8 rather than 6x^2-8x+4