What are Dudeney Numbers?

Dudeney number is named after an English mathematician, Henry Dudeney, who used them in puzzles he created.

What is a Dudeney Number?

Dudeney number is a positive integer that is a perfect cube such that sum of its digits is equal to its own cube root.

For example, 512 is a Dudeney number as

Sum of its digits i.e. 5 + 1 + 2 = 8 and

cube root of 512 = 8 i.e. 8³ = 512.

In total, there are only six Dudeney numbers. They are:

1 ⇒ ∛1 = 1

512 ⇒ (5+1+2) = 8 and ∛512 = 8

4913 ⇒ (4+9+1+3) = 17 and ∛4913 = 17

5832 ⇒ (5+8+3+2) = 18 and ∛5832 = 18

17576 ⇒ (1+7+5+7+6) =26 and ∛17576 = 26

19683 ⇒ (1+9+6+8+3) = 27 and ∛19683 = 27

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