A deck of nine cards can be numbered, so that the sum of the numbers on a randomly chosen pair of cards totals to an integer from 2 to 12 with the same frequency as rolling two standard dice. What are the numbers on the nine cards?
In playing with this, I couldn't seem to find any solutions.
Then it occurred to me that this doesn't have to have integers on
there, so I tried some X.5 numbers, and I quickly realized that if ONE
number is a 0.5 then they all must be (since they could get paired up).
So, I played with those figures a bit, and I quickly came up with the following table:
0.5
1.5
2.5
2.5
3.5
4.5
4.5
5.5
6.5
The following table shows the possible pairings :
notice the frequencies:
2 - 1
3 - 2
4 - 3
5 - 4
6 - 5
7 - 6
8 - 5
9 - 4
10 - 3
11 - 2
12 - 1
0.5 1.5 2.5 2.5 3.5 4.5 4.5 5.5
0.5| XXX XXX XXX XXX XXX XXX XXX XXX
1.5| 2 XXX XXX XXX XXX XXX XXX XXX
2.5| 3 4 XXX XXX XXX XXX XXX XXX
2.5| 3 4 5 XXX XXX XXX XXX XXX
3.5| 4 5 6 6 XXX XXX XXX XXX
4.5| 5 6 7 7 8 XXX XXX XXX
4.5| 5 6 7 7 8 9 XXX XXX
5.5| 6 7 8 8 9 10 10 XXX
6.5| 7 8 9 9 10 11 11 12
|
|
Posted by Thalamus
on 2004-08-09 10:46:35 |
ummm...
