59. Not to the Right Address

- I want to offer you a little puzzle, - said the White Queen. - What I will tell you is a true incident that happened to me recently. Once I needed to send four letters by mail. I wrote four letters, addressed the envelopes, and absent-mindedly placed some of the letters in the wrong envelopes. I put exactly one letter in each envelope. It turned out that I could either send exactly three letters to the correct address, or exactly two letters to the correct address, or exactly one letter to the wrong address.

How many letters did I send to the correct address?

![](https://cdn.mathpix.com/cropped/2024_05_21_5afa4e43618f5800e92dg-076.jpg?height=586&width=965&top_left_y=1409&top_left_x=548)
59. Not to the right address. The statement about exactly three letters (out of four) being sent to the right address means the same as the statement about exactly one letter being sent to the wrong address. Therefore, one has to "choose" between two cases: when exactly three letters and exactly two letters were sent to the wrong address. However, it is impossible to send exactly three letters to the right address, because if three out of four letters are sent to the right address, then the fourth letter is necessarily sent to the right address as well. Therefore, the Queen sent exactly two letters to the right address and exactly two letters to the wrong address.