1) 2758620689655172413793103448

         2) 15

         3)      4 hours, 1 and 1/239 minutes
             or  4 hours, 1 minute, 60/239 seconds

    Notes

  1). Take the unknown number (ending with 8), multiply
      it by 3, and copy each digit of the product into
      the multiplicand. Stop when 8 appears in the
      product without a carry digit.

  2). J + K = 24
      J = 2(K - x)          (x years ago)
      J - x = 0.5(K + y)    (y years hence)
      K + y = 3(J - z)      (z years ago)
      J - z = 3(K - z)

      Solving, J = 15, K = 9, x = 1.5, y = 18, z = 6

  3).    1434 clock minutes = 1440 real minutes
      So  240 clock minutes = 240 X 1440/1434 real minutes
                            = 241 and 6/1434 real minutes
                            = 241 and 1/239 real minutes.

  1. What is the smallest number (greater than 1) which 
     leaves a remainder of 1 when divided by 2, by 3, by
     4, by 5, by 6, by 7 and by 8?

  2. What is the greatest possible number of occasions during
     a year (not a leap year) on which a Friday falls on the
     13th day of a month, and in which months do they occur?

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

         (i)      *1*9             (ii)           ****
               X     *                        X     *3
                 *2*87                           *****
                 =====                          8*575 
                                                ******
                                                ======