Question

Little 1x1x1 cubes are glued together to form a larger nxnxn cube. This larger cube is dumped into a bucket of paint and then allowed to dry. Assuming no paint seeped through any cracks (so only the outside of the nxnxn cube was painted), how many of the little cubes are painted on:
0 faces?
1 face?
2 faces?
3 faces?
4 faces?
5 faces?
6 faces?
Again, this be a puzzle, so justify your answers!

Answer 1

What is sum of the answers you get for the above question? Does this make sense?

Answer 2

This is not a smart question. Or at least the answer choices don't make sense. You ask, "How many of the little cubes are painted on?". Therefore, the answer choices shouldn't have "faces" on them, there should be options for how many cubes were painted...A cube, no matter what the size, has 6 faces. If you dumped it in paint, only 6 faces would be painted on....As far as how many 1 by 1 by 1 cubes were painted....those on the outer edge would have two faces painted....those on the corner edges would have 3 faces painted...those not on the edge or corner would have 1 face painted..... None of them would have all of their faces painted. I hope that makes sense.

Answer 3

The little cubes are glued together, so that only the faces on the outside of the nxnxn cube will get paint on them.

Answer 4

If you read the rest of my post, I explain that

Answer 5

How 'bout it Dalvoron?

Answer 6

well doesn't it all depended on how far the large cube is dunked? If the small cubes are all glued together to form one big nxnxn cube then they are irrelevant to the problem.. but this is puzzle so I am probably wrong lol

Answer 7

Ah, misread. I suppose that the first question mark shouldn't be there. It asks how many of the little cubes are painted on 0 faces? How many are painted on 1 face? etc. Your answer does not contain numbers, so is not satisfactory :)

The entire nxnxn cube is fully immersed in paint.

Answer 8

I think you're wrong. My answer is pretty accurate. You should read it more carefully.

Answer 9

Oh, I understand the question now lol

Answer 10

You have said which parts of the cube are painted on 1 face, 2 faces etc. which is correct. How many cubes does that make in each case?

Answer 11

It's way too late to be thinking about stuff like this. I'm going to bed!

Answer 12

Good night!

Answer 13

It wouldn't be that hard to figure out

There's obviously some pattern to figure out....

....I would start with 1 by 1 by 1....that would have all it's faces painted......

Then 4 by 4 by 4 and figure out how many faces are painted

Then 9 by 9 by 9 etc....

eventually some pattern would emerge. But I don't feel like wasting time figuring it out

Answer 14

The 4x4x4 would have 24 faces painted
The 9x9x9 would have 54 faces painted..
The nxnxn would have n*6 faces painted...

Answer 15

so the pattern is 1 cube, 4 cubes 9 cubes.....n cubes painted

Answer 16

There ya go. A sleepy guy solved your so called puzzle

Answer 17

How many of the 1x1x1 cubes are painted on 0 faces? How many on 1 face? etc :P

Answer 18

What?

Answer 19

Dude, now you're just making stuff up. Give me a medal already

Answer 20

Let's say you have a 4x4x4 cube. As you said before, the corners will have 3 faces painted, the edges will have 2 faces painted. How many 1x1x1 cubes are at the corner / edge / face / middle of the 4x4x4 cube?

Answer 21

If you were going to ask all of these questions, you should have just posted them all at once. I answered your original question, and you still haven't medaled me yet. Don't become a fraud. Just give the appropriate medal for answering the original question. Your latest question should be considered a bonus.

Answer 22

The original question was "how many of the little cubes are painted on: 0 faces? 1 face? 2 faces?" etc

Answer 23

It is not asking for a total number, it is 7 individual questions that have to be individually answered.

Answer 24

Well, in that case I'm going to bed. By the way, you should hire a mathematician to proofread your questions before you make them up

Answer 25

It was given to me by a lecturer, and noone in my class suffered the same issues with understanding it.

Answer 26

Well, I guess all of your classmates also got the answer correct then.

Answer 27

They didn't, but they understood what the problem was asking..

Answer 28

I'm sure your lecturer clarified it enough for them. Apparently you're trying to say that after being presented with the question, no one asked any questions to clarify what was being asked. It's not as straightforward as you think.

Answer 29

look 4 cubes on 3 faces

Answer 30

Perhaps it isn't as straightforward as I think. I thought it was quite clear, but maybe not. Regardless, the question remains unanswered numerically. You have answered it conceptually though.

Answer 31

4 cubes painted on 3 faces is incorrect :(

Answer 32

sry it is 8

Answer 33

Correct!

Answer 34

wait a moment

Answer 35

4/8ths of the question is now complete.

Answer 36

two faces = (n-2*12

Answer 37

sry (n-2)*12

Answer 38

Correct again!

Answer 39

1 face = (n-2)^2 * 6

Answer 40

You're really living up to your name, another point!

Answer 41

0 face = (n-2)^3

Answer 42

is it okay

Answer 43

Yep! That's right. Now just one part of the question is left to answer.

Answer 44

wich

Answer 45

The first reply to the question asks "What is sum of the answers you get for the above question? Does this make sense?"

Answer 46

k

Answer 47

it is n^3

Answer 48

Oh, he's a smart one ;) Correct.

Answer 49

shud i get the medal

Answer 50

I gave you one for your first answer. If I could give more, I would :)

Answer 51

haha