Problem of the Week
for Friday, November 18
Maria found six Go stones that had fallen onto the library floor.Being highly organized,
she put them into three containers which she carefully labeled BB, BW, and WW.
There were two black stones in container BB, two white stones in WW, and one of each color in BW.
Unfortunately, the labels fell off, and when Eva taped them back on, she forgot to check which container was which.
In fact, every container now had the wrong label. When Ragan heard the news, she realized there was a good puzzle here.
What is the fewest number of stones she needs to take out in order to figure out which labels go on which containers?
Gordon's Solution:
| Take one stone out of the box marked BW, if it is black, then the container must be BB because it can’t be WW, or BW because the sticker has to be false. Therefore, it must be BB. You can’t switch the BB sticker with the BW sticker because that would mean that WW would be true. So, you have to switch BW with BB, then switch BW with WW. If the stone you take out is white, then it’s the same reason, just switch BB and WW. |