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?
(In reply to
Quick Guess (Spoiler) by Vernon Lewis)
I got the same answer independently as well. Hopefully, both of us did not make the same mistakes!
Since all 25 numbers appear in the combinations a-o, each top has 5 unique numbers (i.e. no duplicate numbers on different or the same tops).
So, I started with combination a. Since each number is from a different top, I denoted the tops as A-E.
A:1, B:4, C:9, D:10, E:11
From combination f, we know that 18 must be from top A,E and 19 must be on top A,E. From combination l, we know that 19 must be on top A,B, or C since 10 and 11 are known. The only way that both conditions can be satisfied is if 19 is on top A. This means 18 must be on top E.
This same reasoning goes on for the rest of the combinations.
|
|
Posted by gregg
on 2006-10-12 00:08:29 |
re: Quick Guess (Spoiler)
