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

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

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

Archive

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