| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
A knight's tour can be thought of as a cyclic permutation of the elements in an array, with the proviso that each element gets displaced by the distance sqrt(1�+2�). In general, for what sized arrays (mxn) is it possible to find a permutation of elements (not necessarily a cycle) such that each element is displaced by a given distance d = sqrt(p�+q�)? For a given mxn, what is the largest d that permits such a derangement�? �A derangement is a permutation that leaves no element in its original place.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1634.1 | minor point | DESIR::BUCHANAN | Wed Jul 01 1992 11:30 | 10 | |
>For a given mxn, what is the largest d that permits such a derangement�? >�A derangement is a permutation that leaves no element in its original place. Can I propose that you restrict it further, and prohibit 2-cycles as well as one cycles? Otherwise, the keen solver will know he can ignore any 2n-cycles for n>1, since any such could be broken up into n 2-cycles. This seems an undesirable simplication of his task. Just a suggestion, Andrew. | |||||
| 1634.2 | Property of 1634! | COOKIE::MURALI | Sat Jul 18 1992 14:31 | 11 | |
Just an unrelated observation:
1634 = 1^4 + 6^4 + 3^4 + 4^4.
Smallest four digit number with this property.
The other two four digits numbers with the above
property are 8208 and 9474.
Cheers,
Murali.
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| 1634.3 | If he were alive today, he'd turn over in his grave | VMSDEV::HALLYB | Fish have no concept of fire. | Mon Jul 20 1992 10:46 | 1 |
I'll bet Ramanujan knew that, too. | |||||