perplexus.info :: Probability : 2 sums modulo 7

2 sums modulo 7 (Posted on 2016-10-05)

Player A rolls m dice, evaluates the sum of all pips S_a, divides it by 7 and writes down the remainder, say rem_a.
Player B rolls n dice, does the same dividing S_b by 7 and gets rem_b.
i. Evaluate the probability of both remainders being equal.
ii. How does this probability relate to the numbers m and n?

No Solution Yet Submitted by Ady TZIDON

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re(2): some computed values

Comment 3 of 3 |

(In reply to re: some computed values by Charlie)

Using Sloane's OEIS on the previous results (the unreduced numerators), it seems the formula is:

If we define t = m+n, then the probability is

(6^t + 6*((-1)^t))/(7 * 6^t)

Posted by Charlie on 2016-10-05 18:12:19

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