edited 14th Jun '11 2:46:57 PM by alethiophile
edited 13th Jun '11 10:17:36 PM by Tzetze
edited 14th Jun '11 2:50:29 PM by alethiophile
edited 23rd Jun '11 11:00:35 PM by Carciofus
know where they are going, the ones who walk away from Omelas.
edited 23rd Jun '11 11:34:59 PM by Tzetze
Now posting as Motor-Runner.
I have a math/ problem I need to run by you guys. This should be fairly simple and only slightly tricky. When asked to see figures refer to this image◊ A builder using 1x1x1 blocks is building a step pyramid. His first layer (Figure 1) is two squares one inside the other that form the shell of the structure. The outer most layer (black) is 68 blocks on a side. The inner most square grey is 66 blocks on a side. In order to build the pyramid, the next layers outer square will be built on top of the last layers inner square (see figure 2) and a new inner square placed inside that square. See figure two. See Figure 2(The black is the very first outer square, the blue is built on top of the grey layer, the red forms the next layer to built on top of. Other then the two squares the rest of the layer will be empty. The builder needs to build in this manner up to layer 50. At layer 50 the layer will be filled in completely to build the top of the pyramid. How many total individual blocks does the builder need to achieve his goal? The total of all the layers + 317 for interior constructions should give you the final answer.
Part 2 What I have figured out thus far is this. You find the perimeter of both squares for each layer until the 50th layer. The 50th layer will be the area of that layer. To find the area each new layers sides shrink by two. You add up all the perimeter totals for the layers except 50 which is an area. Then add the extra bits for interior structure. I know each layers total for the two perimeters shrinks by a predictable amount. Ie. The first layers total is 536. The next layer is 528. It shrinks by 8 every time. But I have no way to cut the very long process of writing out then calculating that for 49 layers. The 50th layer I think is 19x19 but I think I might be off on that.
What I need is given all this information how many total units will be needed to complete that structure.
edited 12th Aug '11 4:32:15 PM by TuefelHundenIV
edited 12th Aug '11 6:24:24 AM by Deboss
edited 12th Aug '11 10:04:33 AM by Tzetze
edited 12th Aug '11 5:10:10 PM by TuefelHundenIV
edited 13th Aug '11 3:03:16 AM by TuefelHundenIV
edited 15th Aug '11 10:21:21 AM by Rial
edited 15th Aug '11 10:52:58 AM by Rial
edited 15th Aug '11 10:54:00 AM by Tzetze