Henry Ernest Dudeney/Modern Puzzles/94 - Adding their Cubes/Solution
Jump to navigation
Jump to search
Modern Puzzles by Henry Ernest Dudeney: $94$
- Adding their Cubes
- The numbers $407$ and $370$ have this peculiarity, that they exactly equal the sum of the cubes of their digits.
- Thus the cube of $4$ is $64$, the cube of $0$ is $0$, and the cube of $7$ is $343$.
- Add together $64$, $0$ and $343$, and you get $407$.
- Again, the cube of $3$ ($27$), added to the cube of $7$ ($343$), is $370$.
- Can you find a number not containing a nought that will work in the same way?
- Of course, we bar the absurd case of $1$.
Solution
Dudeney gives $153$, but fails to provide $371$.
These are the $3$-digit pluperfect digital invariants, also known as narcissistic numbers or Armstrong numbers.
Historical Note
Martin Gardner, in his $1968$ repackaging 536 Puzzles & Curious Problems, points out the overlooked $371$, then refers to Joseph S. Madachy's Mathematics on Vacation from $1966$, where the general pluperfect digital invariant is discussed.
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $94$. -- Adding their Cubes
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $143$. Adding their Cubes