perplexus.info :: Just Math : Perfect Power Puzzle

Perfect Power Puzzle (Posted on 2015-07-29)

Find all possible 3-digit positive perfect powers that are divisible by the sum of their respective digits.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

There are 11 such 3-digit perfect powers that satisfy the given conditions. These are:
n as pwr s.o.d. 100 10^2 1 144 12^2 9 216 6^3 9 225 15^2 9 243 3^5 9 324 18^2 9 400 20^2 4 441 21^2 9 512 2^9 8 576 24^2 18 900 30^2 9
For an explanation, refer to:
The solution submitted by Charlie in this location.
The solution submitted by Ady TZIDON in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: computer solution	K Sengupta	2024-04-25 08:31:40
re: full solution........................SPOILER	K Sengupta	2024-04-25 08:31:03
re(2): full solution........................SPOILER	Ady TZIDON	2015-07-29 10:23:32
re: full solution........................SPOILER	Charlie	2015-07-29 10:16:47
re: full solution........................SPOILER	Charlie	2015-07-29 10:00:18
computer solution	Charlie	2015-07-29 09:58:22
full solution........................SPOILER	Ady TZIDON	2015-07-29 08:30:27

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