[r-t] Spliced Doubles puzzle

[Philip]

Consider the symmetrical single-hunt doubles methods with

- 3pb making 3rd's to start with and pivoting at the half-lead
- 4th's at the half-lead
- PN 1 or 123 at the lead-head

(e.g. the reverses of St Simons/St Martins etc.)

There are
4 backworks (3.1, 3.145, 345.1, 345.145)
4 frontworks (5.1.145, 5.123.145, 125.1.345, 125.3.145)
2 lead-heads (1, 123)

Any combination gives a valid method with a 3 or 4 lead course, so 4x4x2 
= 32 methods.

It is easy enough to splice 12 methods into an extent: pick a different 
backwork for each 3pb, and a different frontwork for each bell making 
4th's (either 4pb or 5pb, depending on the backwork), and choose the 
lead-heads to join the bits together. 24 methods in two extents is also 
straightforward. But can you fit all 32 into three extents? It seems 
that there ought to be enough freedom to manage it, particularly as the 
first two frontworks are lead splices.

If anyone wants to take up the challenge, I attach the methods and some 
sample extents in siril.

regards,
Philip

5 bells

f85=" 85F",&3.1.5.1.145,+1,"@ \"
u93=" 93U",&3.1.5.1.145,+123,"@ \"
f87=" 87F",&3.1.5.123.145,+1,"@ \"
u95=" 95U",&3.1.5.123.145,+123,"@ \"
f89=" 89F",&3.1.125.1.345,+1,"@ \"
u98=" 98U",&3.1.125.1.345,+123,"@ \"
f90=" 90F",&3.1.125.3.145,+1,"@ \"
u99=" 99U",&3.1.125.3.145,+123,"@ \"
c116="116C",&3.145.5.1.145,+1,"@ \"
v124="124V",&3.145.5.1.145,+123,"@ \"
c118="118C",&3.145.5.123.145,+1,"@ \"
v126="126V",&3.145.5.123.145,+123,"@ \"
c120="120C",&3.145.125.1.345,+1,"@ \"
v129="129V",&3.145.125.1.345,+123,"@ \"
c121="121C",&3.145.125.3.145,+1,"@ \"
v130="130V",&3.145.125.3.145,+123,"@ \"
c147="147C",&345.1.5.1.145,+1,"@ \"
v155="155V",&345.1.5.1.145,+123,"@ \"
c149="149C",&345.1.5.123.145,+1,"@ \"
v157="157V",&345.1.5.123.145,+123,"@ \"
c151="151C",&345.1.125.1.345,+1,"@ \"
v160="160V",&345.1.125.1.345,+123,"@ \"
c152="152C",&345.1.125.3.145,+1,"@ \"
v161="161V",&345.1.125.3.145,+123,"@ \"
f163="163F",&345.145.5.1.145,+1,"@ \"
u171="171U",&345.145.5.1.145,+123,"@ \"
f165="165F",&345.145.5.123.145,+1,"@ \"
u173="173U",&345.145.5.123.145,+123,"@ \"
f167="167F",&345.145.125.1.345,+1,"@ \"
u176="176U",&345.145.125.1.345,+123,"@ \"
f168="168F",&345.145.125.3.145,+1,"@ \"
u177="177U",&345.145.125.3.145,+123,"@ \"

peal="@ \",u98,f90,v161,v155,c149,f87,v126,c116,u171,u177,f167,c120,""
prove peal

peal="@ \",u99,f89,v160,v157,c147,f85,v124,c118,u173,u176,f168,c121,""
prove peal

peal="@ \",u95,f85,c147,u171,u173,f167,v160,c152,f90,v130,v129,c118,""
prove peal

12345  98U
14352  90F
13524 161V
14532 155V
12543 149C
15324  87F
13245 126V
15234 116C
12453 171U
15432 177U
13425 167F
14253 120C
12345
120 rows ending in 12345
Touch is true
12345  99U
14352  89F
13524 160V
14532 157V
12543 147C
15324  85F
13245 124V
15234 118C
12453 173U
15432 176U
13425 168F
14253 121C
12345
120 rows ending in 12345
Touch is true
12345  95U
14352  85F
13524 147C
15432 171U
13425 173U
12453 167F
14532 160V
12543 152C
15324  90F
13245 130V
15234 129V
14253 118C
12345
120 rows ending in 12345
Touch is true