Let k be a positive integer. Suppose that the integers 1, 2, 3, ...3k, 3k + 1 are written down in random order.
What is the probability that at no time during this process, the sum of the integers that have been written up to that time is divisible by 3?
Source: Putnam competition
(In reply to
Solution by Brian Smith)
These are the values I get using Brian's formula:
1 0.250000000
2 0.035714286
3 0.003333333
4 0.000228938
5 0.000012401
for the first five values of k, which disagrees with the direct trials of all possibilities mod 3 in my previous post.
I repeated the case of k=2, using "1234567" instead of "1231231" and got the same results as before: 0.0714286.
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Posted by Charlie
on 2016-03-17 14:47:17 |
re: Solution
