perplexus.info :: Numbers : Another Dudeney problem

Another Dudeney problem (Posted on 2018-03-09)

Dudeney once asked what positive numbers have cube roots equal to the sum of their digits.
Excluding the trivial (i.e. number 1) Dudeney listed five solutions!

Find them!

Hint: the five numbers are below 25000.

See The Solution Submitted by Ady TZIDON

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512 = 8^3 ; 8 = 5 + 1 + 2

4,913 = 17^3 ; 17 = 4 + 9 + 1 + 3

5,832 = 18^3 ; 18 = 5 + 8 + 3 + 2

17,576= 26^3 ; 26 = 1 + 7 + 5 + 7 + 6

19,683= 27^3 ; 27 = 1 + 9 + 6 + 8 + 3

I believe these interesting numbers are named for Dudeney.

Posted by JayDeeKay on 2018-03-09 12:01:11

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