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 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021