4
$\begingroup$

An architect wants to plan the creation of a house, but he has only two perspectives, one from the left and one from the front. The house consists of concrete cubes. All concrete cubes must be connected.

How many cubes does the architect need to build the house, at minimum?

Perspectives, the left one is from the left:

enter image description here

Improve this question
$\endgroup$
0

3 Answers 3

Reset to default
3
$\begingroup$

Assuming that the builder can't circumvent the laws of gravity, so every block must be supported by a block underneath it, the minimum is

8 cubes:

enter image description here

(looking from the front)

Without this assumption, the minimum is

7 cubes:

enter image description here

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ It's 1 or 2 more if all the blocks have to be connected by faces $\endgroup$
    – RShields
    Jun 25, 2019 at 18:14
  • $\begingroup$ Yes, if they have to be connected with their faces. $\endgroup$
    – Matti
    Jun 25, 2019 at 18:17
  • $\begingroup$ Hey, I'm posting here as I literally have no rep on Literature: I put the bounty on expectation that there will be better answers than the ones originally given. The other bounty reasons did not apply so I chose the 'exemplary' one. By far, as you have said is the answer by Christophe. $\endgroup$
    – TheSimpliFire
    Jul 6, 2019 at 18:53
  • $\begingroup$ @TheSimpliFire Gotcha, thanks! When I saw the "exemplary" reason I assumed you'd chosen one of the existing answers to reward. Not sure if you get notifications for new answers to a question you've bountied, so I wanted to ping you and make sure you saw the new one :-) $\endgroup$
    – Rand al'Thor
    Jul 6, 2019 at 18:55
1
$\begingroup$

I am aware that Rand Al Thor has already done the solution with 8 blocks, yet I found a solution that only uses 7 blocks. This solution is compliant with the rule that all the blocks have to be connected by at least one face.

 N/A    N/A    N/A            N/A    N/A    N/A          N/A     block    N/A

block   N/A    N/A            N/A    N/A    N/A          N/A     block   block

block   N/A    N/A            N/A   block   N/A          N/A      N/A    block


       Front                      Side View                    Back View
Improve this answer
$\endgroup$
6
  • $\begingroup$ I think your solution is not quite right. If you place the cube in the middle at the bottom of the house it isn't connected to an other cube with a face. But if you are sure it would be helpful if you send a picture of your building from this website usecubes.com/design $\endgroup$
    – Matti
    Jun 25, 2019 at 20:12
  • $\begingroup$ Oh i'm sorry, I didn't realise that every single cube had to be connected to another cube if it was on the ground. However, would this not put Rand Al Thor's suggestion incorrect? $\endgroup$
    – XDVV
    Jun 25, 2019 at 20:14
  • $\begingroup$ Yes, but @RShiels wrote a comment under his answer where he says that if all cubes have to be connected with their faces it would be one more cube, so I marked his answer as the solution. $\endgroup$
    – Matti
    Jun 25, 2019 at 20:20
  • $\begingroup$ So if they touch the ground, this does not count as a face being connected? It is still touching the ground so it is connecting with at least one face. $\endgroup$
    – XDVV
    Jun 26, 2019 at 14:26
  • $\begingroup$ Touching the ground doesn't count as a connected face. $\endgroup$
    – Matti
    Jun 26, 2019 at 14:48
1
$\begingroup$

9 Cubes, assuming all cubes must be connected face-to-face, not corner-to-corner.

Improve this answer
$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.