Following the practice at Over Pulling one Friday, the vicar of Over Pulling, Rev. Canterbury, came over to Marlene. He was himself a fine ringer and had called a quarter peal of Plain Bob Doubles only a few months previously. The time had come to send it to the "Ringing World" but he couldn't remember the details. He recalled that the band was: Gudgeon Pynn and his wife Polly, Bert Headstock, Rusty Dingler, Marlene Spike and himself. Between them he and Marlene eventually managed to remember the following facts:

    1. Neither of them ever dodged with Rusty,
    2. Bert's bell was bigger than Rev. Canterbury's,
    3. Although Queens and Tittums appeared 11 times each, the quarter was less than 1320,
    4. Polly rang next to Gudgeon,
    5. Marlene ran in at the last bob of the short part whilst Polly made the bob,
    6. Neither Gudgeon nor Bert followed Marlene during Tittums or Queens.

Can you complete the quarter peal details of who rang where, how many changes were rung and what was the composition of the short part?

From 1. Rusty is ringing either 1 or 6.

From 3. There must have been a short part: either 60 or 100. Neither way of ringing 60 produces both Queens and Tittums (as required by the fact that they both occurred 11 times). The touch of 100 is P B P B P x2 or any of its 4 rotations. Three of these will produce both Queens and Tittums: P B P P B x2, P B P B P x2 and B P P B P x2. Thus the quarter peal was 1300.

From 5. and the compositions above we can work out that either Marlene rang the 2nd and Polly the 4th (first one) or that Marlene rang the 4th and polly the 5th (the other two).

Suppose Rusty rang the 6th, and taking 2. and 4. into account. There are three possibilities:

            Rusty Marlene Polly Gudgeon Bert Rev.
        a.     6         2         4         3         5     1
        b.     6         2         4         5         3     1
        c.     6         4         5         6         ?     ?

Option c is ruled out because from 4. we know that Gudgeon would have to ring the 6th, but we have already assumed that Rusty is ringing the 6th. Both a and b are ruled out because either Gudgeon or Bert (on 5th) would follow Marlene (on 2nd) in Tittums, which is ruled out by 6.

Suppose Rusty rang the treble, and taking 2. and 4. into account. There are three possibilities:

            Rusty Marlene Polly Gudgeon Bert Rev.
        a.     1         2         4         3         6     5
        b.     1         2         4         5         6     3
        c.     1         4         5         6         3     2

From 6. we can see that b and c are ruled out because Gudgeon will follow Marlene in Tittums (b) or Queens (c). Only a remains intact and all the information has been used.

Thus the band stood as follows: 1. Rusty, 2. Marlene, 3. Gudgeon, 4. Polly, 5. Rev., 6. Bert. Since we know that Marlene and Polly rang 2nd and 4th we know that the short part was P B P P B x2.

Gudgeon Pynn.
e-mail Gudgeon at gudgeon@pynn_net.clappers

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