mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

If you enjoyed this puzzle, check out Sunday Afternoon Maths VL,
puzzles about floors, or a random puzzle.

Archive

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

Tags

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

Archive

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