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


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


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