mscroggs
.co.uk
mscroggs
.co.uk
blog
puzzles
academic
talks
contact
subscribe
↓ ☰ ↓
Click here to win
prizes
by solving the
mscroggs.co.uk
puzzle Advent calendar.
Click here to win
prizes
by solving the
mscroggs.co.uk
puzzle Advent calendar.
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
odd numbers
consecutive integers
dodecagons
cryptic clues
irreducible numbers
percentages
area
means
balancing
clocks
ave
indices
number
decahedra
geometry
logic
cubics
money
sum to infinity
taxicab geometry
probabilty
albgebra
trigonometry
numbers
digital products
christmas
expansions
coordinates
doubling
circles
floors
addition
calculus
wordplay
square numbers
squares
proportion
perimeter
factorials
dates
crossnumbers
graphs
binary
median
hexagons
axes
digital clocks
speed
pascal's triangle
2d shapes
advent
prime numbers
routes
factors
sequences
tangents
matrices
quadrilaterals
perfect numbers
tournaments
elections
crosswords
multiplication
the only crossnumber
geometric mean
colouring
time
chocolate
integers
people maths
tiling
geometric means
surds
volume
sums
3d shapes
square roots
dice
shapes
rugby
unit fractions
shape
arrows
palindromes
games
mean
averages
regular shapes
angles
sport
lines
sets
combinatorics
star numbers
menace
symmetry
dominos
coins
cube numbers
complex numbers
algebra
range
even numbers
division
scales
triangle numbers
partitions
pentagons
products
gerrymandering
crossnumber
cryptic crossnumbers
digits
differentiation
probability
books
parabolas
integration
multiples
chess
chalkdust crossnumber
cards
triangles
consecutive numbers
grids
quadratics
remainders
bases
functions
fractions
spheres
polygons
determinants
rectangles
planes
ellipses
folding tube maps
polynomials
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
arrows
planes
crossnumbers
indices
regular shapes
routes
ellipses
shape
median
tiling
averages
albgebra
geometry
cryptic clues
the only crossnumber
lines
star numbers
people maths
parabolas
palindromes
volume
shapes
cards
remainders
cryptic crossnumbers
prime numbers
speed
probability
logic
time
3d shapes
angles
complex numbers
matrices
spheres
advent
dice
number
tangents
proportion
taxicab geometry
coordinates
gerrymandering
money
floors
tournaments
bases
products
2d shapes
elections
geometric mean
colouring
menace
partitions
even numbers
functions
quadratics
hexagons
crossnumber
balancing
digits
integers
pascal's triangle
squares
algebra
chocolate
axes
area
dominos
differentiation
means
sum to infinity
factorials
triangle numbers
triangles
unit fractions
chalkdust crossnumber
probabilty
wordplay
integration
square numbers
multiplication
digital products
clocks
range
sums
consecutive integers
polynomials
perfect numbers
division
addition
expansions
quadrilaterals
decahedra
calculus
multiples
surds
determinants
consecutive numbers
doubling
perimeter
mean
factors
numbers
coins
fractions
cubics
polygons
sport
books
dodecagons
geometric means
ave
rectangles
binary
square roots
games
folding tube maps
trigonometry
crosswords
pentagons
dates
chess
circles
digital clocks
christmas
sequences
graphs
combinatorics
percentages
irreducible numbers
rugby
scales
cube numbers
grids
odd numbers
sets
symmetry
© Matthew Scroggs 2012–2024