The numbers 1 and 2 are written on the board. Each day, the scientific consultant Vybegallo replaces the two written numbers with their arithmetic mean and harmonic mean.

a) One day, one of the written numbers (it is unknown which one) turned out to be 941664/665857. What was the other number at that moment?

b) Will the number 35/24 ever be written?
a) 665857/470832: the product of the numbers written on the board is always equal to 2.

b) No: the arithmetic mean decreases each time, while the harmonic mean increases. After the second step, the arithmetic mean will be equal to $17 / 12$ < 35/24, so 35/24 will never be encountered again.

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