Mystery Permutation
- From: "Leroy Quet" <qqquet@xxxxxxxxxxxxxx>
- Date: 1 Sep 2005 14:10:28 -0700
The integers 1 through 10 can be arranged among the variables a(1)
through a(10) so that
(a(1),a(2),a(3),...a(10)) is a permutation of the first 10 integers.
The integers are arranged such that:
*a(1) is a prime.
*a(2) has the same number of 1's in its binary representation as a(1)
has.
*a(3) is divisible by the same number of distinct primes as a(2) is.
*a(5) is the sum of the continued fraction terms of a(4)/a(3).
*a(6) = floor(a(8)*(a(4) +a(5)^2)/a(9)^2).
*a(7)! -a(6)^2 *a(7)^2 = (a(5)^2 -1)*(a(2) -1).
*a(8) = number of distinct primes dividing a(7).
*a(9) = |a(2) - a(1)|.
*a(10) = a(2) + a(1).
I do not know how many different ways the integers can be arranged.
(But there is at least one solution.)
My major challenge for rec.puzzles and sci.math readers is to create
your own such puzzle, with preferably as many variables as possible and
with preferably only one way to arrange the integers among the
variables.
(Be creative.)
thanks,
Leroy Quet
.
- Prev by Date: Re: new online Sudoku solver/game in HTML/javascript
- Next by Date: Tree formations
- Previous by thread: Re: new online Sudoku solver/game in HTML/javascript
- Next by thread: Tree formations
- Index(es):
Relevant Pages
|
