f******e
发帖数: 921 | 1 There are 10 red, 11 blue, 12 green chameleons. Sometimes, two chameleons
meet. If they are the same color, nothing happens. If they are different
colors, they will both change to the third color. Can all chameleons ever
be the same color
any idea? | d********t
发帖数: 9628 | 2
be
No.
【在 f******e 的大作中提到】
: There are 10 red, 11 blue, 12 green chameleons. Sometimes, two chameleons
: meet. If they are the same color, nothing happens. If they are different
: colors, they will both change to the third color. Can all chameleons ever
: be the same color
: any idea?
| f******e
发帖数: 921 | | d********t
发帖数: 9628 | 4
forgot why
【在 f******e 的大作中提到】
: why? thanks!
| D********n
发帖数: 978 | 5 Let red = 0, blue = 1 and green = 2. Consider the remainder of mod 3.
In other words, do all calculations in F3.
Verify:
red + blue = 2*green
red + green = 2*blue
blue + green = 2*red
So all the color changing preserves the remainder of mod 3.
10*red + 11*blue +12*green = 2
However, if they change to the same color, since there are 33 of them, the
total remainder will be 0 for sure. Hence impossible.
be
【在 f******e 的大作中提到】
: There are 10 red, 11 blue, 12 green chameleons. Sometimes, two chameleons
: meet. If they are the same color, nothing happens. If they are different
: colors, they will both change to the third color. Can all chameleons ever
: be the same color
: any idea?
| k*****y
发帖数: 744 | 6 Each move does not change the combination of the numbers Mod 3.
The Initial combination is {1,2,0}. If they were ever in the same color, the
combination should be {0,0,0}.
be
【在 f******e 的大作中提到】
: There are 10 red, 11 blue, 12 green chameleons. Sometimes, two chameleons
: meet. If they are the same color, nothing happens. If they are different
: colors, they will both change to the third color. Can all chameleons ever
: be the same color
: any idea?
| d********t
发帖数: 9628 | 7 对了，谢谢！
the
【在 k*****y 的大作中提到】
: Each move does not change the combination of the numbers Mod 3.
: The Initial combination is {1,2,0}. If they were ever in the same color, the
: combination should be {0,0,0}.
:
: be
| l******i
发帖数: 1404 | 8 首先感谢楼主贡献，
如果可以的话，希望楼主最好能在帖子标题里加上问题的类别和关键词，
例如该帖名字可为：【Brain Teaser】one interview question
这样方便我们工作人员整理，谢谢啦。
我已经把标题改了。
这道题很好，很有启发。 | A**u
发帖数: 2458 | 9 绿皮书
【在 f******e 的大作中提到】
: There are 10 red, 11 blue, 12 green chameleons. Sometimes, two chameleons
: meet. If they are the same color, nothing happens. If they are different
: colors, they will both change to the third color. Can all chameleons ever
: be the same color
: any idea?
| k*****y
发帖数: 744 | 10 Sorry, I was wrong. It is not invariant in general. The correct statement
should be:
If the combination is {0,1,2}, then it is invariant under any move.
the
【在 k*****y 的大作中提到】
: Each move does not change the combination of the numbers Mod 3.
: The Initial combination is {1,2,0}. If they were ever in the same color, the
: combination should be {0,0,0}.
:
: be
|
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