1) 841

         2) Three months, namely February, March, November.

         3) (i)     4129      (ii)         9175
                 X     3              X      93
                   12387                  27525
                   =====                 82575 
                                         853275
                                         ======    

    Notes

  1). The LCM (Least Common Multiple) of 2, 3, 4, 5, 6, 7
      and 8 is 840. So required number is 841.

  2). (One method of several.) Write down the first of each
      month as a day of the year, e.g. 1st Jan = 1, 1st Feb
      = 32, etc. Then reduce these MOD 7 (i.e. remainder
      after dividing by 7).
         JAN = 1         MAY = 2        SEP = 6
         FEB = 4         JUN = 5        OCT = 1
         MAR = 4         JUL = 0        NOV = 4
         APR = 0         AUG = 3        DEC = 6
      The most frequent result, 4, occurs in Feb, Mar and Nov.

  3). By intelligent trial and error.

  1. On 1st Jan. the price of a bottle of my usual brand of
     wine increased by £0.35 to £8.75. But if I consume
     three bottles less this year I shall spend exactly the
     same on wine as last year. How many did I drink then?

  2. The following division sums are correct, but some of 
     the numbers have got lost. Fill in the missing numbers.

      (i)   *)***3              (ii)   **)***9
              1047                         9**
              ====                        ====

  3. The front tyres of my new car should cover 20,000 miles
     before wearing out, while the rear tyres should cover
     30,000 miles. But I intend to interchange the front and
     rear wheels after travelling a certain distance in order
     to equalise the tyre wear. At what mileage should I
     effect the change-over so that all four tyres wear out
     at the same time?