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