Ravi has designed plans for a castle that show the front, top, and side views.
Build a castle to Ravi’s design using the cubes.
What is the largest number of cubes that you can use in the construction of a castle from Ravi’s plans?
What is the smallest number of cubes that you can use in the construction of a castle from Ravi’s plans?
Solution
Here we show one possible castle that could be made from Ravi’s design.
This castle looks exactly the same from each side. It has 22 blocks.
Actually this is the most blocks that can be used for Ravi’s design. If any other block is added, then either the front or side view will be wrong.
There may be some dispute as to what constitutes the smallest castle. We assume that blocks can not float - they need to have one beneath them to hold them up. Given that, we have shown the smallest number of cubes in the castle below.
By having ‘towers’ in opposite corners the castle has the correct front and side views. This castle has 14 blocks. Is this the only smallest castle?
Extension
Can you build a symmetrical castle that is different from any of the ones you have built so far? How many symmetrical castles can you build to the Ravi’s specifications?