Math Forum - Problem of the Week


How Many Cubes?

Here are the front view and side view of some cubes that I arranged.

Questions:
What is the largest number of cubes that I could have used to make this arrangement?
 
What is the smallest number of cubes that I could have used to make this arrangement?

Here's a Java applet from the National Library of Virtual Manipulatives to help you think about the possible arrangements:
    Space Blocks http://matti.usu.edu/mathforum/spaceblocks.html

Instructions for using Space Blocks:

Note: Applet works best using Internet Explorer or Netscape.
 
Add blocks
Add blocks to the workspace by clicking and dragging them from the block bin in the upper-right corner.
 
Remove blocks
Remove blocks from the workspace by clicking and dragging them to the trash in the lower-right corner.
 
Change perspective
Change your perspective (the point in the space from which you view the blocks) by clicking and dragging in any empty area of the workspace.
 
Connect blocks
Connect a yellow block to a blue block by dragging it near a blue block until you see one of the sides of the blue block turn red. Then let go of the yellow block and it will be glued to the red side of the blue block. To unglue a block, click and drag it away.
 
Sometimes it may be hard to see where you are putting a block because you can't see through it. Hold down the Shift key while dragging a block to make it transparent - you'll then see the block in outline form to help you place it.

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