106. I Have a Bag, With Some Balls in it
I have a bag, with some balls in it. All but 4 are blue, all but 4 are green, and all but 4 are red. How many balls do I have in total?
Submitted by tartle · Added 20 November 2009
Solution:
The total number of balls in the bag is 6. You can have 2 blue, 2 green, and 2 red balls. This configuration satisfies the conditions that all but 4 are blue, all but 4 are green, and all but 4 are red.
Comments (10)
Six
5. right?
12
6 balls.
This is basically an english language problem, there's not much logic in this.
Lets say there are x balls
So,
Number of blue balls = x-4
Number of green balls = x-4
Number of red balls = x-4
Total number of balls = 3x-12
But we took the original number of balls to be x.
Therefore,
3x-12=x
or, x=6
The problem does not say that there are only blue, green, and red balls. There may be balls of other colors. In that case, there could be 1 blue, 1 green, 1 red, and 2 of other colors (say black and white).
Using einsteinager's math, this would look like:
Let x = total number of balls
Number of blue balls = x-4
Number of green balls = x-4
Number of red balls = x-4
Number of other colored balls = y
x = 3(x - 4) + y
x = 3x - 12 + y
2x = 12 - y
The only restriction on y is that it cannot be greater than x.
Values of y that produce positive integer results for x, with x >= y are:
y = {0, 2, 4}
Thus, there could be 2 other colored balls, and a total of 5 balls.
You could even logically say that there could be 4 balls of other colors, and no blue/green/red balls.
If the problem were to state that the bag only has blue, green, and red balls, then y would be 0, and the answer would be 6.
4 because all but 4 are blue, green and red at the same time. Impossible, so these balls can't exist. This leaves 4 unaffected by this, so only four can exist in the bag.
The first guy got it right... six
2 blue, 2 green, 2 red
that means 2 blue and 4 that are NOT blue (red and green together)
therefore all but 4 are blue
same with other colors
there are more than 12 balls or just 12 balls in the bag
6 balls
6 balls
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