perplexus.info :: Numbers : Pandigital and Pretty Powerful V

Pandigital and Pretty Powerful V (Posted on 2023-04-20)

Determine all triplets (X, Y, Z) of base 12 positive integers such that the duodecimal representation of X^Y*(X+1)^Z has no leading zeroes and contains each of the digits from 0 to B exactly once, with the restriction that: at least one of Y and Z is different from 1.

What is the total number of such triplets without any restriction?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

There are precisely two triplets given by:
(X,Y, Z) = (1BB, 4,1), (A084, 2,1),so that:
1BB^4 * 1BA^1 = 2740936815BA
and A084^2 * A085^1 = 70962B1345A8
For an explanation, refer to the computer program assisted solution submitted by Charlie in this location.

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

Subject	Author	Date
re: solution, I hope	Charlie	2023-04-20 22:06:24
solution, I hope	Charlie	2023-04-20 21:48:13

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info