Bag of Balls
A bag contains 9 colored balls: 3 red, 3 yellow, and 3 green. Three balls are removed from the bag, one at a time.
1. The first and third ball removed were not a pair of yellow and green.
2. A green ball was removed before a red one, if and only if, a yellow was taken after a red.
3. A green was not removed later than a red one.
4. The first color removed was different from both the second and third.
What color were the 3 balls removed from the bag ... and in what order were they taken?
1. The first and third ball removed were not a pair of yellow and green.
2. A green ball was removed before a red one, if and only if, a yellow was taken after a red.
3. A green was not removed later than a red one.
4. The first color removed was different from both the second and third.
What color were the 3 balls removed from the bag ... and in what order were they taken?
posted by Zaux at
9:39 PM
2 Comments:
Bag of Balls
1. The first and third ball removed were not a pair of yellow and green.
2. A green ball was removed before a red one, if and only if, a yellow was taken after a red.
3. A green was not removed later than a red one.
4. The first color removed was different from both the second and third.
Abbrieviate red,yellow green as R,Y,G
Assume 1st ball R.
2nd ball:
-R violates rule 4
-Y violates rule 2
-G violates rule 3
1st ball R invalid
Assume 1st ball Y.
2nd ball:
-R ok
-Y violates rule 4
-G ok
For YR:
3rd ball
-R ok
-Y violates rule 4
-G violates rule 3
YRR is a valid solution.
For YG:
-R violates rule 2
-Y violates rule 4
-G violates rule 1
YG invalid
Assume 1st ball G.
2nd ball:
-R ok
-Y ok
-G violates rule 4
For GR:
3rd ball
-R violates rule 2
-Y violates rule 1
-G violates rule 4
GR invalid
For GY:
3rd ball
-R violates rule 2
-Y violates rule 1
-G violates rule 4
GY invalid
Thus only YRR is valid.
Answer:
1st ball Yellow
2nd ball Red
3rd ball Red
Cam
Hi Cam ... correct you are.
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