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# Puzzles

## Integer part

Let $$\lfloor x\rfloor$$ denote the integer part of $$x$$ (eg. $$\lfloor 7.8\rfloor =7$$).
When are the following true:
a) $$\lfloor x+1\rfloor = \lfloor x\rfloor + 1$$
b) $$\lfloor nx\rfloor = n\lfloor x\rfloor$$ (where $$n$$ is an integer)
c) $$\lfloor x+y\rfloor = \lfloor x\rfloor +\lfloor y\rfloor$$
d) $$\lfloor xy\rfloor = \lfloor x\rfloor \lfloor y\rfloor$$

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