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 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025