A perfect gift for a girl
Aloysius and Amos are Brenda's good friends. One day, the three of them were shopping when the two boys came across an array of 10 containers which came in 4 different colours and 6 different shapes:
- Blue crescent, blue square, blue triangle
- Golden heart, golden star
- Green circle, green square, green triangle
- Red circle, red heart
The boys thought of buying one of the containers for Brenda. Brenda commented, "Exactly one of the containers is in both my favourite colour and favourite shape." She separately told Aloysius and Amos her favourite colour and shape respectively.
Aloysius said, "I still do not know which container you want and Amos, I am sure you cannot tell either."
Amos said, "At first, I was not sure but based on what you said, Aloysius, I know already."
Aloysius said, "Then I also know now."
Assuming both boys are perfectly logical, which container do you think Brenda is eyeing?
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1 solution
For Aloysius to be fully sure that Amos can't tell, Aloysius must be told a color which has all its shapes duplicated. If Aloysius was told a color which has at least one unique shape, then there is a chance that Amos can tell for sure. To be precise, if Aloysius was told blue, then there is a chance Amos can pinpoint the desired container as one of the blue containers is in a crescent shape which makes it unique. Similarly, if Aloysius was told golden, then Amos may be able to zero in on the correct container as he might be told star of which there is only one unique container.
Hence Brenda’s favourite colour is neither blue nor golden. It is either green or red. Amos must be told a shape which is unique otherwise he can't tell for sure which container. This rules out the round containers which come in green and red, the two possible colors.
Note that Aloysius was sure for the second time he spoke. This means he must be told a color which has only two possible shapes as the round containers in both colors have been ruled out so by elimination, the only possibility is the container in the other shape. Since green has three shapes while red only has two, he must be told red. So Brenda's favourite colour is red.
Since the red circle is out, Brenda must be eyeing the r e d h e a r t .