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It's not the blue jar, since marbles were taken from the middle
jar and placed into the blue jar. This leaves purple and green.
Only an even number of marbles can be split in half.
After removing 3 marbles, the remaining marbles
must be capable of being split into half (even number).
Comments (4)
Here's a concise solution:
a. The Blue Jar is excluded because marbles are moved to it from the Middle Jar.
b. The Green Jar had an even number of marbles, doubling those in the Purple Jar. Removing three results in an odd number, not divisible by two.
c. Only the Purple Jar fits, as it could have had an odd number, allowing an even number post-removal of three marbles, suitable for halving. Therefore, the Purple Jar must be the correct answer.
The last statment doesn't exclude the blue jar from being in the middle jar. Jenny could have simply taken half the marbles out of it, then putting them back in.
Hi Max,
The following statement:
"She then removed half of the remaining marbles from the middle jar and placed them into the blue jar. " does not allow for the interpretation that the marbles are removed and then placed back into the same jar.
It definitively indicates that the marbles are moved from one jar, specifically the middle jar, to a different jar, in this case, the blue jar.
This excludes the possibility of the blue jar being the middle jar as noted in the first hint.
The remainder is halved after removing 3 marbles from the middle jar. This shows that the
middle jar had an odd number of marbles. The middle jar is not green since the green jar had an even number of marbles (twice the purple marbles implies the number is even); removing 3 marbles would make a split impossible. The middle jar is not blue, since marbles were removed from the middle jar and placed into blue. Therefore the middle jar is purple.
Prior to removal we know that just the green jar contained an even number of marbles. Therefore the middle jar is purple.