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

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

Archive

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