<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div>On Sun, 2021-02-14 at 16:53 +0000, Philip Saddleton wrote:</div><blockquote type="cite" style="margin:0 0 0 .8ex; border-left:2px #729fcf solid;padding-left:1ex"><div>On Thu, 2021-02-04 at 21:56 +0000, Richard Pullin wrote:</div><blockquote type="cite" style="margin:0 0 0 .8ex; border-left:2px #729fcf solid;padding-left:1ex"><div dir="ltr">On eight bells there are 384 mirror rows, the permitted place notations being 18, 36, 1458, 1278, 3456, 123678, X. The nicest of these are 18, 36, X, but it seems you can only attain 192 rows using just these place notations, in much the same way that you can only ring 60 rows in Doubles without using single changes. </div></blockquote><div><br></div><div>The reason for this is that the changes that the even change (X) keeps bells in the same half of the row, while the odd ones swap a pair in 4-5. So the possible rows are the in course ones with an even number of bells in the half they started in, and the out of course ones with an odd number.</div></blockquote><div><br></div><div>This is true of the whole group - what I meant to say is that if bells in the wrong half of the row are swapped with their partner, if an odd number of swaps is required then each half of the resultant row will be out of course.</div><div><br></div><blockquote type="cite" style="margin:0 0 0 .8ex; border-left:2px #729fcf solid;padding-left:1ex"><div><br></div><div>I came up with this: <a href="https://complib.org/method/41162?accessKey=a829c83566f003025dcb638e01a32df35e3064e1" style="font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 12px; orphans: 2; white-space: nowrap; widows: 2; background-color: rgb(245, 245, 245);">https://complib.org/method/41162?accessKey=a829c83566f003025dcb638e01a32df35e3064e1</a> - which I believe is the only possibility for a palindromic method with Original lead heads. It has similarities with Quick Six Triples: ring quick sixes at front and back with double dodging in the middle, then replace 18 with x when it would come round.</div></blockquote><div><br></div><div>This can be extended by effectively singling in the opposite block with a pair of places in 45, though to keep it palindromic we lose the Original lead heads or have to finish with x:</div><div><div><span style="color: rgb(51, 51, 51); font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 12px; font-variant-ligatures: normal; orphans: 2; white-space: nowrap; widows: 2; background-color: rgb(245, 245, 245); text-decoration-thickness: initial;"><a href="https://complib.org/method/41177?accessKey=12b86791088e5b6b4f0de546418aae0278ddd015">https://complib.org/method/41177?accessKey=12b86791088e5b6b4f0de546418aae0278ddd015</a></span></div></div><div><br></div><div>I think this would best be rung with 14 bobs.</div><div><br></div><div>PABS</div><div><br></div><div><span></span></div></body></html>