Apartments in Blocky Country
In "Blocky Country", the apartments are built using square blocks.
An apartment is built with some unit cubes are stacked atop a flat 4 by 4 square. Suppose the maximum of cubes used to be
a
and the minimum number of cubes used to be
b
that could be in the stacks. The figures show views of the stacks from two different sides. What would be the value of
a + b
?
- I get the idea from a question in USAMTS, but I have rephrased and tweaked the givens for this question, so don't try to search for an answer ;)
The answer is 59.
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1 solution
We don't have to draw a 3D diagram in order to solve this question. Simply construct two 4x4 tables as the bird-eyes' view for the apartment would be enough.
The table is the bird-eyes' view for the building and the number surrounding it shows how much blocks are seen in that direction. So the blocks build on that line should be smaller or equal to that number with at least one block reaching that height.