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) \(\lfloor xy\rfloor = \lfloor x\rfloor \lfloor y\rfloor \)

Show answer & extension


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


lines factors probabilty angles graphs elections percentages scales cryptic clues products factorials parabolas routes trigonometry odd numbers cube numbers dice books chalkdust crossnumber taxicab geometry the only crossnumber number indices 3d shapes regular shapes money hexagons rectangles differentiation grids triangles crossnumber perfect numbers chocolate numbers palindromes doubling triangle numbers sport prime numbers time people maths area functions 2d shapes square numbers complex numbers means clocks christmas coordinates speed balancing crosswords shape surds symmetry digits logic median ave addition digital clocks polygons menace partitions rugby planes dates floors sequences crossnumbers sums cryptic crossnumbers dodecagons perimeter arrows division calculus geometry range ellipses quadratics cards square roots multiplication advent chess integers coins proportion multiples gerrymandering star numbers squares remainders folding tube maps spheres mean averages volume irreducible numbers shapes probability algebra games integration pascal's triangle fractions dominos bases wordplay sum to infinity circles unit fractions colouring tiling


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020