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- #1

- Jan 26, 2012

- 4,041

1. (0.51,0.51,0.51)

2. (0.61,0.71,0.71)

3. (0.68,0.68,0.68)

4. (0.49,0.49,0.49)

--------------------

Remember to read the POTW submission guidelines to find out how to submit your answers!

- Thread starter Jameson
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- Thread starter
- Admin
- #1

- Jan 26, 2012

- 4,041

1. (0.51,0.51,0.51)

2. (0.61,0.71,0.71)

3. (0.68,0.68,0.68)

4. (0.49,0.49,0.49)

--------------------

Remember to read the POTW submission guidelines to find out how to submit your answers!

- Thread starter
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- #2

- Jan 26, 2012

- 4,041

Solution (from Stackexchange):

$d$: A>B>C

$e$: A>C>B

$f$: B>A>C

$g$: B>C>A

$h$: C>A>B

$i$: C>B>A

From this, $a = d + e + f$, $b = f + g + i$, and $c = e + h + i$.

$a + b +c = d + 2e + 2f + g + h + 2i \le 2(d + e + f + g + h + i) = 2(\text{# of voters})$.

In scenario (3), $a + b + c = 204\%$, which is impossible.

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