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 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019