mscroggs
.co.uk
mscroggs
.co.uk
blog
puzzles
academic
talks
contact
subscribe
subscribe
Loading image...
Puzzles
121
Source:
Mathematical Circus
by Martin Gardner
Find a number base other than 10 in which 121 is a perfect square.
Show answer & extension
Hide answer & extension
This is true for any base larger than 2. This is because:
$$121_n = 1+2n+n^2$$ $$=(n+1)^1$$
Extension
Which other base 10 square numbers are always square in high enough bases?
Tags:
numbers
,
bases
If you enjoyed this puzzle, check out
Sunday Afternoon Maths XLIV
,
puzzles about
numbers
, or
a random puzzle
.
Archive
Show me a random puzzle
Most recent collections
Advent calendar 2023
Advent calendar 2022
Advent calendar 2021
Advent calendar 2020
List of all puzzles
Tags
tangents
multiples
crossnumber
trigonometry
sequences
ave
games
partitions
people maths
irreducible numbers
means
median
division
speed
range
menace
dice
even numbers
indices
factorials
consecutive integers
differentiation
geometric mean
perfect numbers
shape
volume
albgebra
pascal's triangle
complex numbers
rectangles
chocolate
mean
coordinates
angles
dodecagons
probabilty
binary
spheres
chess
factors
odd numbers
grids
hexagons
sport
numbers
advent
star numbers
square roots
cryptic crossnumbers
triangles
quadratics
square numbers
proportion
rugby
remainders
graphs
lines
shapes
tournaments
coins
probability
chalkdust crossnumber
folding tube maps
arrows
wordplay
tiling
area
perimeter
averages
surds
time
colouring
decahedra
palindromes
books
number
fractions
addition
taxicab geometry
elections
3d shapes
integers
triangle numbers
prime numbers
calculus
multiplication
the only crossnumber
bases
doubling
crosswords
gerrymandering
sums
circles
floors
money
cryptic clues
digital clocks
digits
algebra
polynomials
axes
products
cubics
geometry
scales
dominos
parabolas
quadrilaterals
ellipses
combinatorics
matrices
dates
squares
determinants
cube numbers
planes
routes
consecutive numbers
christmas
unit fractions
2d shapes
digital products
logic
functions
geometric means
regular shapes
percentages
cards
integration
symmetry
crossnumbers
pentagons
clocks
sum to infinity
polygons
expansions
balancing
sets
Archive
Show me a random puzzle
▼ show ▼
▲ hide ▲
Most recent collections
Advent calendar 2023
Advent calendar 2022
Advent calendar 2021
Advent calendar 2020
List of all puzzles
Tags
logic
irreducible numbers
arrows
geometric mean
differentiation
scales
squares
elections
rugby
the only crossnumber
median
perfect numbers
colouring
palindromes
square numbers
pascal's triangle
digits
advent
probabilty
angles
quadratics
sets
number
unit fractions
time
regular shapes
speed
parabolas
sum to infinity
expansions
coins
dodecagons
remainders
addition
indices
digital clocks
menace
wordplay
crossnumber
combinatorics
proportion
circles
multiples
even numbers
complex numbers
tournaments
triangle numbers
chess
cube numbers
averages
determinants
geometric means
trigonometry
perimeter
integers
routes
star numbers
bases
coordinates
partitions
chalkdust crossnumber
cryptic clues
functions
books
hexagons
balancing
calculus
taxicab geometry
doubling
tiling
people maths
odd numbers
volume
planes
numbers
triangles
sport
multiplication
crossnumbers
cryptic crossnumbers
shapes
division
prime numbers
polygons
products
shape
christmas
albgebra
floors
percentages
mean
integration
money
dice
games
sequences
range
graphs
decahedra
geometry
axes
folding tube maps
spheres
rectangles
3d shapes
fractions
crosswords
surds
lines
gerrymandering
dominos
cubics
clocks
square roots
area
means
factorials
ellipses
2d shapes
cards
algebra
binary
matrices
consecutive numbers
tangents
sums
dates
chocolate
consecutive integers
digital products
probability
symmetry
grids
quadrilaterals
pentagons
polynomials
factors
ave
© Matthew Scroggs 2012–2024