Problems Drive Solutions

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.
   0	0	15
   0	10	5
   0	0	5
   0	5	0
   6	5	0
   0	5	6
   6	5	6
   1	10	6
   1	1	15

   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)

   

   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:-

    

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

Reproduced from Eureka 27 pages 39-40.
HTML conversion Copyright © 2002-4 The Archimedeans.

Return to Eureka 27 home page
Return to Eureka home page
Return to Archimedeans home page