perplexus.info :: Just Math : Boxed real number range

Boxed real number range (Posted on 2025-04-24)

Determine all possible values of the expression x - [x/2] - [x/3] - [x/6] by varying x in the real numbers.

No Solution Yet Submitted by Danish Ahmed Khan

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solution

| Comment 1 of 3

Graphing shows the value plotted as stright line segments ranging from 0 to 3.

(0+6*k,0) to (2+6*k,2)

(2+6*k,1) to (3+6*k,2)

(3+6*k,1) to (4+6*k,2)

(4+6*k,1) to (6+6*k,3)

with k a non-negative integer and being equal for any beginning/ending pair.

The beginning points are included, but the ending points are not, so the overall range is [0, 3).

Posted by Charlie on 2025-04-24 16:55:39

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