The numbers 1 to 25 appear randomly on the sides of five pentagonal spinning tops. If all five tops are spun at the same time, the following results could occur.
a) 1 4 9 10 11 b) 2 4 17 21 22 c) 2 11 12 16 24
d) 3 5 16 19 23 e) 3 18 19 24 25 f) 4 9 10 18 19
g) 4 10 18 20 22 h) 4 17 18 19 22 i) 6 10 16 22 23
j) 7 19 22 24 25 k) 8 13 16 18 19 l)10 11 12 14 19
m)10 15 19 21 22 n)10 16 18 20 22 o)13 15 18 19 22
Which five numbers appear on each top?
The numbers appear on the tops:
1-2-6-19-20
3-8-9-12-22
4-14-15-16-25
5-10-13-17-24
7-11-18-21-23
This was obtained as follows:
1. a) and f) both have 4 9 10 so either 1 or 11 must be paired with either 18 or 19
from l) 11 can
't be with 19 so it must be 11-18 and 1-19
2. f) and g) both have 4 10 18 so 9 or 19 with 20 or 2
from j) 19 not with 22 so 1-19-20 and 9-22
3. f) and h) both have 4 18 19 so 9 or 10 with 17 or 22
from 2) above we know 9-22 so 10-17
4. g) and n) both have 10 18 20 22 so 4-16
5. k) and o) both have 13 18 19 so 8 or 16 with 15 or 22
from n) 16 not with 22 so 8-9-22 and 4-15-16
6. m) and o) both have 15 19 22 so 10 or 21 with 13 or 18
from n) 10 not with 18 so 10-13-17 and 11-18-21
7. e) and j) both have 19 24 25 so 3 or 18 with 7 or 22
from n) 18 not 22 so 3-8-9-22 and 7-11-18-21
8. from b) 2 not with 4 17 21 22 so 1-2-19-20
9. from c) and l) 12 is not with 10 11 16 19 so 3-8-9-12-22
10. from l) 14 not with 10 11 12 19 so 4-14-15-16
11. from d) and i) 23 not 3 10 16 19 so 7-11-18-21-23
12. from d) 5 is not with 3 16 19 23 so 5-10-13-17
13. from i) 6 is not with 10 16 22 23 so 1-2-6-19-20
14. from c) 24 is not with 2 11 12 16 so 5-10-13-17-24
15. from e) 25 is not with 3 18 19 24 so 4 -14-15-16-25
Edited on October 16, 2006, 6:29 am
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Posted by Lisa
on 2006-10-16 06:27:44 |
Solution
