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Assigning a wonky die (Posted on 2006-04-28) Difficulty: 2 of 5
I have an unfair die whose sides are known to have the following probabilities:{.02,.04,.08,.12,.24,.5}
Assign the numbers {1,2,3,4,5,6} to these sides so the expected roll is the same as for a fair die.

Can you solve this without brute force?

See The Solution Submitted by Jer    
Rating: 3.0000 (1 votes)

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Some solutions by hand Comment 4 of 4 |
I managed to find 4 solutions by hand. To start with, I multiplied both sides (the sum of the probabilities and 3.5) by 50 so I was working with integers, which gave:

a + 2b + 4c + 6d + 12e + 25f = 175

I then worked out the minimum and maximum possibilities with f being 1..6. This eliminated f=1 and f=6 and gave definite solutions for f=2 (134562) and f=5 (643215).

Playing guess and check with f=3 and f=4 I found 246153 and 526134, but had no idea if they were the only ones or not. Evidently (see Charlie's comment) not!
  Posted by snark on 2006-05-03 22:29:34
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