Brain-Teaser 504

From The Sunday Times, 7th February 1971 [link]

The inter-house Scrumps competition has just ended at Marlinghurst School. The four houses play each other once and the scoring is on a league basis (win 2, draw 1, lose 0). Arne played Bach in the 1st round, Chopin in the 2nd and Debussy in the 3rd.

In the 1st round no two houses scored the same number of “scrumps” (a scrump is a sort of goal scored by forcing an opponent through a hole in the wall).

In the 2nd and 3rd rounds every house scored exactly twice as many scrumps as its current opponent had scored in the previous round.

Chopin and Debussy tied on points, but a better scrump average (i.e. ratio of scrumps for to scrumps against) gave Debussy the Pergolesi Bowl. Arne and Bach also tried, but Arne’s lower scrump average put them fourth in the final table.

Although the total number of scrumps scored in the competition fell short of the school record (55) it was higher than last year’s total (44).

What was:

(a) Arne’s scrump average?
(b) the score in the Bach-Chopin match?

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