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Using Cards as Dice (Posted on 2004-08-09) Difficulty: 2 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 2.7500 (4 votes)

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Solution ummm... | Comment 3 of 9 |
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
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