Problems Drive Solutions

Five minutes were allowed for each question. The average marks (out of ten) obtained by the 24 pairs competing are given in brackets. The highest total was 48.
  1. (5.6) One point given per prime.
  2. (0.1) 3 p.m. (3 × 51 + 27 minutes past noon).
  3. (5.2) (a) 18, 20 (prime numbers plus one).
    (b) 18 (81 reversed).
    (c) 53104 (= 2312 - 162).
    (d) 74 (sum of the fifth terms of the other three series). [Alternative solution: 163 (second differences are 21).]
  4. (1.3)
    6 pt.10 pt.15 pt.
    0015
    0105
    005
    050
    650
    056
    656
    1106
    1115

    No one discovered this! However, four pairs gained half marks for a solution one move longer.

  5. (0.5) 19. Again, no fully correct solutions.
  6. (0.0)

    [diagram]

    Maximum distance is 59/18 units as shown. No one discovered any of the best FOUR arrangements.

  7. (0.4) a = b = c = d = 11.
  8. (4.5) (a) 1/3, (b) 1/3, (c) 2/3, (d) 1/2.
  9. (5.5) 6.
  10. (3.6) Four cities, as in the diagram below:-

    [diagram]

  11. ( . ) 13.
  12. (0.1) 8 years. Sister's present age, 5, satisfies 8/3 < 5 < 8 8/9.

Reproduced from Eureka 27 pages 39-40.
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