Dudeney number
Encyclopedia
A Dudeney number is a positive integer
that is a perfect cube such that the sum of its decimal digits
is equal to the cube root of the number. There are exactly six such integers :
1 = 1 x 1 x 1 ; 1 = 1
512 = 8 x 8 x 8 ; 8 = 5 + 1 + 2
4913 = 17 x 17 x 17 ; 17 = 4 + 9 + 1 + 3
5832 = 18 x 18 x 18 ; 18 = 5 + 8 + 3 + 2
17576 = 26 x 26 x 26 ; 26 = 1 + 7 + 5 + 7 + 6
19683 = 27 x 27 x 27 ; 27 = 1 + 9 + 6 + 8 + 3
The name derives from Henry Dudeney
, who noted the existence of these numbers in one of his puzzles, Root Extraction, where a professor in retirement at Colney Hatch
postulates this as a general method for root extraction.
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
that is a perfect cube such that the sum of its decimal digits
Digit sum
In mathematics, the digit sum of a given integer is the sum of all its digits,...
is equal to the cube root of the number. There are exactly six such integers :
1 = 1 x 1 x 1 ; 1 = 1
512 = 8 x 8 x 8 ; 8 = 5 + 1 + 2
4913 = 17 x 17 x 17 ; 17 = 4 + 9 + 1 + 3
5832 = 18 x 18 x 18 ; 18 = 5 + 8 + 3 + 2
17576 = 26 x 26 x 26 ; 26 = 1 + 7 + 5 + 7 + 6
19683 = 27 x 27 x 27 ; 27 = 1 + 9 + 6 + 8 + 3
The name derives from Henry Dudeney
Henry Dudeney
Henry Ernest Dudeney was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the country's foremost creators of puzzles...
, who noted the existence of these numbers in one of his puzzles, Root Extraction, where a professor in retirement at Colney Hatch
Colney Hatch
Colney Hatch is the historical name for a small district within the London Borough of Barnet in London, England. The name Colney Hatch was originally that of a hamlet in the parish of Friern Barnet, first recorded in the early 15th century...
postulates this as a general method for root extraction.