I recently stumbled upon these really cool puzzles, at mathsnet (http://mathsnet.net/geometry/solid/houses.html)
It’s quite interesting and a fun change from the regular work.
So, give your brain a treat, and try those puzzles. :-)
If you found it hard, I have few tips and a little strategy below.
I tried some of those puzzles and though of a simple strategy that would make things easier.
- Fill up the whole cube.
- Remove all must be removed – from the empty position in the views, we can decide which blocks must be removed.
- Mark which blocks MUST stay.
- Are there any block that should be definitely removed?
- yes -> remove all such blocks *
- no -> remove an unmarked block at random **
- Is numebr of blocks higher than the target?
- yes -> go to step 3
- no -> Stop
Fig1:figuur1 target
* Identifying blocks that should definitely be removed:
When deciding what block to remove, it is important first to identify how many redundancies there are in each plane.
Forexample, in figuur1 (problem 1 ), you can see that all the views (front, right, top) has 12 blocks each(Fig1), and the number of available blocks to build it is also 12. Hence, we know, there are no redundant blocks in any plane. i.e. no 2 blocks are sharing the same line.
In figuur3, we can see that front, right views has 12 blocks each, while top view has ony 8 blocks (Fig2).
- Fig2:figuur3 target
Hence, we identify that none of the blocks should be sharing any horizontal lines, but there would be more than one block sharing some vertical lines.So, if there are any blocks that are marked as ‘must stay’ is sharing such a line(where there should be no redundant blocks) with an unmarked block, we know the unmarked block should definitely be removed.
**Due to the symmetry of the problem, if there aren’t any blocks that should definetely be removed, randomly removing an unarked block would not affect the solution.
I found this method of filling the cube and breaking it up afterwards easier than filling it up to match the views.
Solving figuur3, with screen-shots explaining the strategy.
1.
2.
3. The blocks marked with a black dot are the ones that should definitely stay.
4.
In this figure, the block that was in the square marked in a black cross was removed. (at random).
You can see how this introduced new blocks that MUST stay. (marked with red dots). (step 3 , in 2nd iteration)
And as discussed earlier, since there shouldn’t be any redundant blocks in the horizontal plane, the blocks marked in red crosses should be removed.(step 4, in 2nd iteration)
By continuing this method, you can achieve at the final target, with 12 cubes. :)
Many thanks to mathsnet.net for the cool puzzles!!!
