# Dudeney number

Dudeney number

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 (sequence A061209 in OEIS):

```    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.

## References

• H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1968, p 36.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• number game — Introduction       any of various puzzles and games that involve aspects of mathematics.       Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved.… …   Universalium

• Henry Dudeney — Born Henry Ernest Dudeney 10 April 1857(1857 04 10) Mayfield, East Sussex, England Died 23 April 1930 …   Wikipedia

• 500 (number) — For other uses, see 500 (disambiguation). ← 499 501 → 500 List of numbers Integers …   Wikipedia

• Alice Dudeney — Born Alice Whiffin 21 October 1866(1866 10 21) Brighton, England, U.K. Died 21 November 1945(1945 11 21) (aged 81) Lewes, England, U.K. Pen name Alice Dudeney, Mrs. Henry …   Wikipedia

• Narcissistic number — In recreational number theory, a narcissistic number[1][2] (also known as a pluperfect digital invariant (PPDI),[3] an Armstrong number[4] (after Michael F. Armstrong)[5] or a plus perfect number) …   Wikipedia

• List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… …   Wikipedia

• Rook polynomial — Despite its name, the rook polynomial is used not only to solve chess recreational problems but also in a number of problems arising in combinatorial mathematics, group theory, and number theory.The coefficients of the rook polynomial represent… …   Wikipedia

• Computer-assisted language learning — (CALL) is succinctly defined in a seminal work by Levy (1997: p. 1) as the search for and study of applications of the computer in language teaching and learning .[1] CALL embraces a wide range of ICT applications and approaches to teaching… …   Wikipedia

• Verbal arithmetic — Verbal arithmetic, also known as alphametics, cryptarithmetic, crypt arithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters.… …   Wikipedia

• Tangram — For other uses, see Tangram (disambiguation). Like most modern sets, this wooden tangram is stored in the square configuration. The tangram (Chinese: 七巧板; pinyin: qī qiǎo bǎn; literally seven boards of skill ) is a dissection puzzle consisting of …   Wikipedia

### Share the article and excerpts

##### Direct link
Do a right-click on the link above
and select “Copy Link”