Hi,
please don't double-post again.
You're wasting the time of the helpers.
Consider a collection of piles of bananas consisting of one pile of 9 bananas, one pile of 6, and one pile of 2. Such a collection, denoted as C1, could be expresswed as (9, 6, 2). Obtain a new collection, C2, by harvesting C1, where harvesting is defined to mean remove one banaba from each pile to form a new pile. Thus we have C2 = (8, 5, 3, 1), and if C2 is harvested we obtain:
C3 = (7, 4, 4, 2).
a) Let C1 = (8, 5, 2) and determine C100.
b) Let C1 = (7, 6, 5) and determine C1995
THANKS IN ADVANCE FOR YOUR HELP!!!!
Hello, rlarach!
I don't know of any formula to solve these,
. . but I got them by some primitive Brute Force.
(a) I listed the first few cases and found a pattern . . .Consider a collection of bananas: a pile of 9 bananas, a pile of 6, and a pile of 2.
Such a collection, denoted as:
Obtain a new collection, , by harvesting , where harvesting is defined
. . to mean remove one banana from each pile to form a new pile.
Thus we have: .
And if is harvested, we obtain: .
a) Let . .Determine
b) Let . .Determine
After the first three steps, the sequence enters a three-step cycle.
We have: .
Hence, equals the first term of the cycle.
Therefore: .
(b) I did the same here . . .
After the first two steps, the sequence enters a six-step cycle.
We have: .
Hence, equals the first term of the cycle.
Therefore: .