1) 75 bottles

         2) (i)  9)9423          (ii)   11)9999
                   1047                     909
                   ====                    ====

         3) 12,000 miles

    Notes

  1). If I drank n bottles last year,

           8.40 n = 8.75 (n - 3)
      Solving,  n = 75

  2). By trial and error.

  3). Each front tyre uses 1/20000 of a tread per mile, and
      each rear tyre uses 1/30000 of a tread per mile. So
      total tread used per mile = 2/20000 + 2/30000 = 1/6000.
      There are four treads to use.
      So total distance covered = 4 X 6000 = 24000 miles.
      Interchange tyres after half this mileage.

  1. I drive five miles to work each morning through heavy
     traffic. If I could drive 10 mph faster the journey
     would take 5 mins. less. How fast do I normally travel?

  2. Choose five numbers from this set of ten so that they
     add together to give 300:
        37, 42, 43, 51, 60, 65, 84, 87, 88, 98

  3. (a) My secretary typed four letters, and four
     corresponding envelopes. She put one letter into each
     envelope, but not one was in its correct envelope. In
     how many ways could she do this?
     (b) The following day she had six letters to type, and
     again got every one into a wrong envelope. In how many
     ways could she do this?