Check out Glinski's Hexagonal Chess, our featured variant for May, 2024.

Enter Your Reply

The Comment You're Replying To
V. Reinhart wrote on Sat, Apr 8, 2017 05:40 PM UTC:

A huygens is chess piece that jumps in the directions of a rook any prime number of squares. In this discussion, I also impose the limit that it has a minimum jump distance of 5 or more squares (as it is used in Trappist-1 ).

So this huygens jumps distances of 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97... and so on. Its icons are shown here:

Icon 1 - by Fergus Duniho.

Icon 2 - Scientific Version

Just like a knight sometimes has trouble moving to a certain square (like requiring 4 jumps to move to a square 2 squares up and 2 left), moving a huygens can also take a few jumps to move to certain squares. Moving an odd number of squares can be tricky if the number isn't prime, because the sum of two primes is always even (unless one of the numbers is 2, but the huygens here can't jump 2 squares). So in these cases, a huygens needs to make 3 jumps to get to a particular square.

When moving an even number of squares, I think it would usually take 2 jumps. But I don't know if there is a way to prove this for every even-numbered move. It is currently unknown if every even integer can be expressed as the sum of two primes. In the 1700's Christian Goldbach believed it was true but couldn't prove it. Today it is still an unsolved problem and is known as the Goldbach Conjecture.

So if you are playing a game of chess with the huygens, don't always assume that you can move an even number of squares in two jumps. There may be some rare cases where three jumps are required. But shorter moves are usually not a problem to figure out. Here's a summary I believe is usually true:
  If the distance is prime (5 or more) the huygens can move there in one jump.
  If the distance is even, the huygens can get there in two jumps (always or almost always true)
  If the distance is odd and not prime, it will require three jumps
The list below shows how to do it for distances up to 40. This may not include every possible method for each distance. For some short moves, it is necessary to overjump the destination, and them move back.

(Move/Leap distances to make the move):
1  (5,7,-11)
2  (7,-5)
3  (5,11,-13)
4  (11,-7)
5  (5)
6  (11,-5)
7  (7)
8  (13,-5)
9  (5,11,-7)
10 (5,5) or (17,-7)
11 (11)
12 (5,7)
13 (13)
14 (7,7)
15 (5,5,5)
16 (5,11)
17 (17)
18 (5,13) or (7,11)
19 (19)
20 (7,13)
21 (7,7,7)
22 (5,17) or (11,11)
23 (23)
24 (5,19) or (7,17) or (11,13)
25 (5,7,13)
26 (7,19) or (13,13)
27 (5,11,11) or (5,5,17) or (7,7,13)
28 (5,23) or (11,17)
29 (29)
30 (7,23) or (11,19) or (13,17)
31 (31)
32 (13,19)
33 (11,11,11)
34 (17,17) or (11,23)
35 (11,11,13)
36 (17,19)
37 (37)
38 (11,11,11,5)
39 (13,19,7)
40 (11,29) or (17,23)

If anyone finds an error or a faster way for any of these moves please leave a reply.


Edit Form
Conduct Guidelines
This is a Chess variants website, not a general forum.
Please limit your comments to Chess variants or the operation of this site.
Keep this website a safe space for Chess variant hobbyists of all stripes.
Because we want people to feel comfortable here no matter what their political or religious beliefs might be, we ask you to avoid discussing politics, religion, or other controversial subjects here. No matter how passionately you feel about any of these subjects, just take it someplace else.
Quick Markdown Guide

By default, new comments may be entered as Markdown, simple markup syntax designed to be readable and not look like markup. Comments stored as Markdown will be converted to HTML by Parsedown before displaying them. This follows the Github Flavored Markdown Spec with support for Markdown Extra. For a good overview of Markdown in general, check out the Markdown Guide. Here is a quick comparison of some commonly used Markdown with the rendered result:

Top level header: <H1>

Block quote

Second paragraph in block quote

First Paragraph of response. Italics, bold, and bold italics.

Second Paragraph after blank line. Here is some HTML code mixed in with the Markdown, and here is the same <U>HTML code</U> enclosed by backticks.

Secondary Header: <H2>

  • Unordered list item
  • Second unordered list item
  • New unordered list
    • Nested list item

Third Level header <H3>

  1. An ordered list item.
  2. A second ordered list item with the same number.
  3. A third ordered list item.
Here is some preformatted text.
  This line begins with some indentation.
    This begins with even more indentation.
And this line has no indentation.

Alt text for a graphic image

A definition list
A list of terms, each with one or more definitions following it.
An HTML construct using the tags <DL>, <DT> and <DD>.
A term
Its definition after a colon.
A second definition.
A third definition.
Another term following a blank line
The definition of that term.