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# Sunday Afternoon Maths VL

Posted on 2015-08-02

## 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) $$\lfloor xy\rfloor = \lfloor x\rfloor \lfloor y\rfloor$$

## Make the sums

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums reading across and down are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, $$4+3\times2$$ is 14, not 10.
 + - = 4 + - × - × = 27 - × ÷ × ÷ = 16 =2 =8 =6
Tags: numbers, grids
If you enjoyed these puzzles, check out Advent calendar 2019,
puzzles about taxicab geometry, or a random puzzle.

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