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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

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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

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    $\begingroup$ It's 1 or 2 more if all the blocks have to be connected by faces $\endgroup$ – RShields Jun 25 at 18:14
  • $\begingroup$ Yes, if they have to be connected with their faces. $\endgroup$ – Matti Jun 25 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 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 at 18:55
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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
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  • $\begingroup$ 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 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 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 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 at 14:26
  • $\begingroup$ Touching the ground doesn't count as a connected face. $\endgroup$ – Matti Jun 26 at 14:48
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9 Cubes, assuming all cubes must be connected face-to-face, not corner-to-corner.

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