Gathering the beans Problem 335Published on Saturday, 23rd April
2011, 04:00 pm; Solved by 295 Whenever Peter feels bored, he
places some bowls, containing one bean each, in a circle. After
this, he takes all the beans out of a certain bowl and drops
them one by one in the bowls going clockwise. He repeats this,
starting from the bowl he dropped the last bean in, until the
initial situation appears again. For example with 5 bowls he
acts as follows: So with 5 bowls it takes Peter 15 moves to
return to the initial situation. Let M(x) represent the number
of moves required to return to the initial situation, starting
with x bowls. Thus, M(5) = 15. It can also be verified that
M(100) = 10920. Find M(2k+1). Give your answer modulo 79.