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


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


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