K. 335. A peculiar calculator only has four buttons on it: (eight plus root seven), (addition), (reciprocal) and (equals) (see the figure).
The calculator always carries out the operations with exact values, and it can also store the current value as a constant if the button is pressed twice. That is, in subsequent calculations whenever the button is pressed, the number is incremented by that value any number of times. (E.g. if the buttons are pressed, it will display ). Prove that the result of the following sequence of operations is 1:
... (56 times)
... (15 times)
This problem is for grade 9 students only.
Deadline expired on 10 April 2012.